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Proceedings of the American Mathematical Society

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

 
 

 

Nonstratifiable regular quotients of separable stratifiable spaces


Author: Eric K. van Douwen
Journal: Proc. Amer. Math. Soc. 52 (1975), 457-460
MSC: Primary 54E20
DOI: https://doi.org/10.1090/S0002-9939-1975-0375247-9
MathSciNet review: 0375247
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Abstract: A regular quotient of a countable $ {M_1}$-space need not be stratifiable, and a regular first countable quotient of a first countable separable $ {M_1}$-space need not be stratifiable either. This answers a question of Borges. The second example depends on a new, simple, example of a first countable separable nonmetrizable $ {M_1}$-space.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0375247-9
Keywords: Regular quotient, stratifiable, separable, first countable, $ {M_1}$-space
Article copyright: © Copyright 1975 American Mathematical Society

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