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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A symmetrizable space that is not perfect


Author: Dennis A. Bonnett
Journal: Proc. Amer. Math. Soc. 34 (1972), 560-564
MSC: Primary 54A25
DOI: https://doi.org/10.1090/S0002-9939-1972-0295275-9
MathSciNet review: 0295275
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Abstract: An example is given of a Hausdorff symmetrizable space which has a closed subset that is not a $ {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}$-space Y having a point $ {x_0}$ such that $ \{ {x_0}\} $ is not a $ {G_\delta }$-subset of Y.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0295275-9
Keywords: Abstract spaces, symmetrizable, semimetrizable, $ {G_\delta }$-subset, subparacompact, perfect space
Article copyright: © Copyright 1972 American Mathematical Society