Pub Date : 1979-05-01DOI: 10.1016/0016-660X(79)90003-5
R.J. Daverman , S.A. Pax
The first part of this paper supplements earlier work of the first-named author by exhibiting an example of a wild n-sphere Σ in En+1 (n⩾4) for which each horizontal n-dimensional hyperplane of En+1 that does meet Σ intersects it either in a point or in an (n − 1)-sphere that is flatly embedded in the hyperplane. The second part sets forth an improved criterion for detecting the n-cell (n ≠ 4) based upon properties of slices determined as inverse sets associated with maps of a space to an interval.
{"title":"Cross sectionally simple spheres can be wild","authors":"R.J. Daverman , S.A. Pax","doi":"10.1016/0016-660X(79)90003-5","DOIUrl":"10.1016/0016-660X(79)90003-5","url":null,"abstract":"<div><p>The first part of this paper supplements earlier work of the first-named author by exhibiting an example of a wild <em>n</em>-sphere <em>Σ</em> in <em>E</em><sup><em>n</em>+1</sup> (<em>n</em>⩾4) for which each horizontal <em>n</em>-dimensional hyperplane of <em>E</em><sup><em>n</em>+1</sup> that does meet <em>Σ</em> intersects it either in a point or in an (<em>n</em> − 1)-sphere that is flatly embedded in the hyperplane. The second part sets forth an improved criterion for detecting the <em>n</em>-cell (<em>n</em> ≠ 4) based upon properties of slices determined as inverse sets associated with maps of a space to an interval.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 2","pages":"Pages 139-146"},"PeriodicalIF":0.0,"publicationDate":"1979-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90003-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74210881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90026-6
Robert J. Daverman
This paper presents an example of a shrinkable (in the sense of Bing) cellular upper semi-continuous decomposition of a non-metric Hausdorff 2-manifold V such that the associated decomposition space is a 2-manifold topologically distinct from V.
{"title":"Shrinkable decompositions of non-metric manifolds can produce other manifolds","authors":"Robert J. Daverman","doi":"10.1016/0016-660X(79)90026-6","DOIUrl":"10.1016/0016-660X(79)90026-6","url":null,"abstract":"<div><p>This paper presents an example of a shrinkable (in the sense of Bing) cellular upper semi-continuous decomposition of a non-metric Hausdorff 2-manifold <em>V</em> such that the associated decomposition space is a 2-manifold topologically distinct from <em>V</em>.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 27-31"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90026-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75409160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90029-1
H.B. Keynes , M. Sears
An initial investigation in -expansion relative to families of continuous functions on the acting group is presented, modelled after previous work of Bowen and Walters on real flows. Basic properties are established, and expansion in the natural class of non-trivial homomorphisms is extensively studied. Finally, modelling discrete flows with such expansion in symbolic subshifts is investigated. Generalizations to Rn and Zn are indicated.
{"title":"F-Expansive transformation groups","authors":"H.B. Keynes , M. Sears","doi":"10.1016/0016-660X(79)90029-1","DOIUrl":"10.1016/0016-660X(79)90029-1","url":null,"abstract":"<div><p>An initial investigation in <span><math><mtext>F</mtext></math></span>-expansion relative to families of continuous functions on the acting group is presented, modelled after previous work of Bowen and Walters on real flows. Basic properties are established, and expansion in the natural class of non-trivial homomorphisms is extensively studied. Finally, modelling discrete flows with such expansion in symbolic subshifts is investigated. Generalizations to <strong>R</strong><sup>n</sup> and <strong>Z</strong><sup>n</sup> are indicated.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 67-85"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90029-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86088091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90027-8
Temple H. Fay, Edward T. Ordman, Barbara V. Smith Thomas
In this paper we investigate the topological structure of the Graev free topological group over the rationals. We show that this free group fails to be a k-space and fails to carry the weak topology generated by its subspaces of words of length less than or equal to n. As tools in this investigation we establish some properties of net convergence in free groups and also some properties of certain canonical maps which are closely related to the topological structure of free groups.
{"title":"The free topological group over the rationals","authors":"Temple H. Fay, Edward T. Ordman, Barbara V. Smith Thomas","doi":"10.1016/0016-660X(79)90027-8","DOIUrl":"10.1016/0016-660X(79)90027-8","url":null,"abstract":"<div><p>In this paper we investigate the topological structure of the Graev free topological group over the rationals. We show that this free group fails to be a <em>k</em>-space and fails to carry the weak topology generated by its subspaces of words of length less than or equal to <em>n</em>. As tools in this investigation we establish some properties of net convergence in free groups and also some properties of certain canonical maps which are closely related to the topological structure of free groups.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 33-47"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90027-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86068166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90024-2
Józef Chaber
An approach to the theory of subparacompactness is presented here. This approach allows one to understand the notions of subexpandability and to generalize a theorem from [6]. We also give an answer to a question from [5].
{"title":"On subparacompactness and related properties","authors":"Józef Chaber","doi":"10.1016/0016-660X(79)90024-2","DOIUrl":"10.1016/0016-660X(79)90024-2","url":null,"abstract":"<div><p>An approach to the theory of subparacompactness is presented here. This approach allows one to understand the notions of subexpandability and to generalize a theorem from [6]. We also give an answer to a question from [5].</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 13-17"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90024-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76380413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90025-4
D.W. Curtis, Vo-Thanh-Liem
{"title":"Infinite products which are homeomorphic to Hilbert space","authors":"D.W. Curtis, Vo-Thanh-Liem","doi":"10.1016/0016-660X(79)90025-4","DOIUrl":"10.1016/0016-660X(79)90025-4","url":null,"abstract":"","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 19-25"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90025-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82639459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90032-1
Mary E. Rudin
No square of a Souslin line or tree is hereditary normal.
苏斯林线或树的正方形都不是遗传正常的。
{"title":"Hereditary normality and souslin lines","authors":"Mary E. Rudin","doi":"10.1016/0016-660X(79)90032-1","DOIUrl":"10.1016/0016-660X(79)90032-1","url":null,"abstract":"<div><p>No square of a Souslin line or tree is hereditary normal.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 102-105"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90032-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78589690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90030-8
Ronnie Levy
Conditions assuring that a compact space is a compactification of the rationals are given. Relations between the π-weight and strong density are discussed.
给出了保证紧空间是有理的紧化的条件。讨论了π重与强密度之间的关系。
{"title":"Compactifications of the rationals and small compact spaces","authors":"Ronnie Levy","doi":"10.1016/0016-660X(79)90030-8","DOIUrl":"10.1016/0016-660X(79)90030-8","url":null,"abstract":"<div><p>Conditions assuring that a compact space is a compactification of the rationals are given. Relations between the π-weight and strong density are discussed.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 87-91"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90030-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85818594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90031-X
Leonard R. Rubin, R.M. Schori, John J. Walsh
Dimension theory for separable metric spaces is approached using the concept of essential families (for example, the n pairs of opposite faces of the n-cube). A new theory of essential families is developed and is used to construct examples of infinite-dimensional compacta that contain no closed n-dimensional (n ⩾ 1) subsets; these constructions are conceptually much easier than previous ones. Also, the theory is used to construct easy examples of n-dimensional, totally disconnected spaces.
{"title":"New dimension-theory techniques for constructing infinite-dimensional examples","authors":"Leonard R. Rubin, R.M. Schori, John J. Walsh","doi":"10.1016/0016-660X(79)90031-X","DOIUrl":"10.1016/0016-660X(79)90031-X","url":null,"abstract":"<div><p>Dimension theory for separable metric spaces is approached using the concept of essential families (for example, the <em>n</em> pairs of opposite faces of the <em>n</em>-cube). A new theory of essential families is developed and is used to construct examples of infinite-dimensional compacta that contain no closed <em>n</em>-dimensional (<em>n</em> ⩾ 1) subsets; these constructions are conceptually much easier than previous ones. Also, the theory is used to construct easy examples of <em>n</em>-dimensional, totally disconnected spaces.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 93-102"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90031-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79349139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1979-02-01DOI: 10.1016/0016-660X(79)90022-9
Andrew J. Berner
Four classes of spaces are considered, all generalizing quasi-k spaces.The implications among these classes under the assumptions that the spaces are Hausdorff, regular, and normal are briefly discussed. A regular relatively bi-quasi-k space which is not quasi-k is constructed, answering a question of Olson. The continuum hypothesis is used to construct a relatively quasi-k space that is not quasi-k.
{"title":"Generalizations of quasi-k spaces","authors":"Andrew J. Berner","doi":"10.1016/0016-660X(79)90022-9","DOIUrl":"10.1016/0016-660X(79)90022-9","url":null,"abstract":"<div><p>Four classes of spaces are considered, all generalizing quasi-<em>k</em> spaces.The implications among these classes under the assumptions that the spaces are Hausdorff, regular, and normal are briefly discussed. A regular relatively bi-quasi-<em>k</em> space which is not quasi-<em>k</em> is constructed, answering a question of Olson. The continuum hypothesis is used to construct a relatively quasi-<em>k</em> space that is not quasi-<em>k</em>.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 1-6"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90022-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72669485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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