A symmetrizable space that is not perfect-Reference-Cited by-同舟云学术

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A symmetrizable space that is not perfect

Published:1972 Issue:2 Volume:34 Page:560-564
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bonnett Dennis A.

Abstract

An example is given of a Hausdorff symmetrizable space which has a closed subset that is not a G δ {G_\delta } -subset (thus, it is not perfect) and which is not subparacompact. This example is then used in the construction of a symmetrizable T 1 {T_1} -space Y having a point x 0 {x_0} such that { x 0 } \{ {x_0}\} is not a G δ {G_\delta } -subset of Y.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-034-02/S0002-9939-1972-0295275-9/S0002-9939-1972-0295275-9.pdf

Reference9 articles.

1. Behavior of metrizability in factor mapping;Arhangel′skiĭ, A.;Dokl. Akad. Nauk SSSR,1965

2. Mappings and spaces;Arhangel′skiĭ, A. V.;Russian Math. Surveys,1966

3. Bicompact sets and the topology of spaces.;Arhangel′skiĭ, A. V.;Trudy Moskov. Mat. Ob\v{s}\v{c}.,1965

4. Subparacompact spaces;Burke, Dennis K.,1970

5. D. K. Burke and R. A. Stoltenberg, Some properties of 𝜋-images of metric spaces (to appear).

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Spaces and mappings;Open Problems in Topology II;2007

2. Gσ-sets in symmetrizable and related spaces;General Topology and its Applications;1978-11

3. On F-spaces;General Topology and its Applications;1978-07

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