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Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants 对于序不变量和基数不变量，伪开函数是单调递减的
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90028-4
James R. Boone

A new property of pseudo-open functions is presented in this paper. Pseudo-open functions are monotonic decreasing with respect to ordinal and cardinal invariants defined by compact and sequential closures. A weak form of continuity, called k-continuous, is defined, characterized and used in the proof of the monotonicity properties of pseudo-open mappings. The relationships between the classes of k-continuous and sequentially continuous mappings in the category of all topological spaces and the continuous mappings in the subcategories of k-spaces and sequential spaces are presented.

本文给出了伪开函数的一个新性质。伪开函数相对于紧闭包和序闭包定义的序数和基数不变量是单调递减的。定义了连续性的一种弱形式，称为k-连续，并将其特征化，用于伪开映射单调性的证明。给出了所有拓扑空间范畴中k-连续和序列连续映射的类与k-空间和序列空间的子范畴中连续映射的关系。
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引用次数: 3
Gσ-sets in symmetrizable and related spaces 对称及相关空间中的g σ-集
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90029-6
S.W. Davis, G. Gruenhage, P.J. Nyikos

In this paper we answer questions of Arhangel'skii and Michael by providing an example of a regular symmetrizable space which is not subparacompact and has a closed subset which is not a Gσ-set. We also use the idea of sequential order to obtain some positive results, and several examples are provided which show that these results are in some sense the best possible.

本文给出了一个正则对称空间的例子，该空间不是次副紧的，并且有一个非gσ集的闭子集，从而回答了Arhangel’skii和Michael的问题。我们还利用顺序的思想得到了一些积极的结果，并给出了几个例子，表明这些结果在某种意义上是最好的。
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引用次数: 24
Contractibility of Whitney continua in C(X) C(X)中Whitney连续体的可缩性
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90031-4
Ann Petrus
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引用次数: 27
Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants 对于序不变量和基数不变量，伪开函数是单调递减的
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90028-4
James R. Boone
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引用次数: 3
Gσ-sets in symmetrizable and related spaces 对称及相关空间中的g σ-集
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90029-6
S. W. Davis, G. Gruenhage, P. Nyikos
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引用次数: 24
Martin's axiom and normality 马丁公理和正态性
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90030-2
I. Juhász, W. Weiss
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引用次数: 11
Contractibility of Whitney continua in C(X) C(X)中Whitney连续体的可缩性
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90031-4
Ann Petrus

We show that there are Whitney maps on the 2-cell such that Whitney continua in the hyperspace of the 2-cell are non-contractible, non-locally contractible, and have non-trivial Čhech cohomology in dimension 2. This implies that contractibility, local contractibility, being an AR, being an ANR, and acyclicity in Čech cohomology are not Whitney properties. We show, however, that contractibility is a Whitney property for the class of dendrites.

我们证明了2-cell上存在Whitney映射，使得2-cell的超空间中的Whitney连续体是不可收缩的，非局部可收缩的，并且在2维空间中具有非平凡Čhech上同调。这意味着可收缩性、局部可收缩性、是AR、是ANR和Čech上同调中的不环性不是惠特尼性质。然而，我们证明了树突类的可收缩性是惠特尼性质。
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引用次数: 27
A completeness property of some function spaces 一些函数空间的完备性
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90027-2
S. S. Khurana
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引用次数: 0
Statistical metric spaces as related to topological spaces 与拓扑空间相关的统计度量空间
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90026-0
B. Morrel, J. Nagata
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引用次数: 33
A note on a theorem of arhangel'skiǐ 关于arhangel' skiy的一个定理的注解
General Topology and its Applications
Pub Date : 1978-11-01 DOI: 10.1016/0016-660X(78)90024-7
M. Ismail
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引用次数: 3
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