Pub Date : 2024-01-02DOI: 10.14712/1213-7243.2023.023
Oleg Lihvoinen
{"title":"On extensions of families of operators","authors":"Oleg Lihvoinen","doi":"10.14712/1213-7243.2023.023","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.023","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"79 19","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139390424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-02DOI: 10.14712/1213-7243.2023.026
Ioana Ghenciu
{"title":"Isomorphic properties in spaces of compact operators","authors":"Ioana Ghenciu","doi":"10.14712/1213-7243.2023.026","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.026","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"136 19","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139452982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-02DOI: 10.14712/1213-7243.2023.021
Abir Kicha, H. Damak, M. A. Hammami
{"title":"Practical $h$-stability behavior of time-varying nonlinear systems","authors":"Abir Kicha, H. Damak, M. A. Hammami","doi":"10.14712/1213-7243.2023.021","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.021","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"76 5","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139452315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.14712/1213-7243.2023.012
Yoshito Ishiki
Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.
{"title":"Metric trees in the Gromov--Hausdorff space","authors":"Yoshito Ishiki","doi":"10.14712/1213-7243.2023.012","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.012","url":null,"abstract":"Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"42 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.14712/1213-7243.2023.017
Rodrigo Hidalgo Linares, Oleg Okunev
We study the relation of $L$-equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an $L$-retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify $L$-retracts in various classes of topological spaces. As applications, we present a method for constructing examples of $L$-equivalent mappings and $L$-equivalent spaces and in particular, we show that the properties of being an open mapping or a perfect mapping are not $L$-invariant.
{"title":"Free locally convex spaces and $L$-retracts","authors":"Rodrigo Hidalgo Linares, Oleg Okunev","doi":"10.14712/1213-7243.2023.017","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.017","url":null,"abstract":"We study the relation of $L$-equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an $L$-retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify $L$-retracts in various classes of topological spaces. As applications, we present a method for constructing examples of $L$-equivalent mappings and $L$-equivalent spaces and in particular, we show that the properties of being an open mapping or a perfect mapping are not $L$-invariant.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"40 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.14712/1213-7243.2023.018
Stoyu T. Barov
Let ${mathbb{V}}$ be a separable real Hilbert space, $k in {mathbb{N}}$ with $k < dim {mathbb{V}}$, and let $B$ be convex and closed in ${mathbb{V}}$. Let ${mathcal{P}}$ be a collection of linear $k$-subspaces of ${mathbb{V}}$. A point $w in B$ is called exposed by ${mathcal{P}}$ if there is a $P in {mathcal{P}}$ so that $(w + P) cap B ={w}$. We show that, under some natural conditions, $B$ can be reconstituted as the convex hull of the closure of all its exposed by ${mathcal{P}}$ points whenever ${mathcal{P}}$ is dense and $G_{delta}$. In addition, we discuss the question when the set of exposed by some ${mathcal{P}}$ points forms a $G_{delta}$-set.
设${mathbb{V}}$为可分离实数希尔伯特空间，$k in {mathbb{N}}$与$k < dim {mathbb{V}}$，并设$B$为${mathbb{V}}$中的凸闭空间。设${mathcal{P}}$是${mathbb{V}}$的线性$k$ -子空间的集合。如果有$P in {mathcal{P}}$点，则称为${mathcal{P}}$暴露点$w in B$，以便$(w + P) cap B ={w}$。我们证明，在某些自然条件下，当${mathcal{P}}$是致密的和$G_{delta}$时，$B$可以被重构为其所有暴露于${mathcal{P}}$点的闭合的凸包。此外，我们还讨论了一些${mathcal{P}}$点暴露的集合何时构成$G_{delta}$ -集合的问题。
{"title":"More on exposed points and extremal points of convex sets in $mathbb{R}^n$ and Hilbert space","authors":"Stoyu T. Barov","doi":"10.14712/1213-7243.2023.018","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.018","url":null,"abstract":"Let ${mathbb{V}}$ be a separable real Hilbert space, $k in {mathbb{N}}$ with $k < dim {mathbb{V}}$, and let $B$ be convex and closed in ${mathbb{V}}$. Let ${mathcal{P}}$ be a collection of linear $k$-subspaces of ${mathbb{V}}$. A point $w in B$ is called exposed by ${mathcal{P}}$ if there is a $P in {mathcal{P}}$ so that $(w + P) cap B ={w}$. We show that, under some natural conditions, $B$ can be reconstituted as the convex hull of the closure of all its exposed by ${mathcal{P}}$ points whenever ${mathcal{P}}$ is dense and $G_{delta}$. In addition, we discuss the question when the set of exposed by some ${mathcal{P}}$ points forms a $G_{delta}$-set.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"84 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136346640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.14712/1213-7243.2023.020
Jindrich Zapletal
It is consistent that ZF+DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles in two-dimensional Euclidean space does not.
{"title":"Coloring triangles and rectangles","authors":"Jindrich Zapletal","doi":"10.14712/1213-7243.2023.020","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.020","url":null,"abstract":"It is consistent that ZF+DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles in two-dimensional Euclidean space does not.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"8 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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