DISCRETE REFLEXIVITY IN GO SPACES

被引:5
|
作者
Tkachuk, Vladimir V. [1 ]
Wilson, Richard G. [1 ]
机构
[1] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City 09340, DF, Mexico
关键词
Discretely reflexive property; discretely Lindelof space; GO space; discretely locally compact space; discretely Cech-complete space; d-separable space; discretely scattered space; linearly ordered space;
D O I
10.3336/gm.49.2.15
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A property P is discretely reflexive if a space X has P whenever (D) over bar has P for any discrete set D subset of X. We prove that quite a few topological properties are discretely reflexive in GO spaces. In particular, if X is a GO space and (D) over bar is first countable (paracompact, Lindelof, sequential or Frechet-Urysohn) for any discrete D subset of X then X is first countable (paracompact, Lindelof, sequential or Frechet-Urysohn respectively). We show that a space with a nested local base at every point is discretely locally compact if and only if it is locally compact. Therefore local compactness is discretely reflexive in GO spaces. It is shown that a GO space is scattered if and only if it is discretely scattered. Under CH we show that Cech-completeness is not discretely reflexive even in second countable linearly ordered spaces. However, discrete Cech-completeness of X x X is equivalent to its Cech-completeness if X is a LOTS. We also establish that any discretely Cech-complete Borel set must be Cech-complete.
引用
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页码:433 / 446
页数:14
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