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Proceedings of the American Mathematical Society

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

 

 

Quotient and pseudo-open images of separable metric spaces


Author: Paul L. Strong
Journal: Proc. Amer. Math. Soc. 33 (1972), 582-586
MSC: Primary 54B15; Secondary 54E35
MathSciNet review: 0300253
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Abstract: Ernest A. Michael has given a characterization of the regular quotient images of separable metric spaces. His result is generalized here to a characterization of the $ {T_1}$ quotient images of separable metric spaces (which are the same as the $ {T_1}$ quotient images of second countable spaces). This result is then used to characterize the Hausdorff pseudo-open images of separable metric spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0300253-7
Keywords: Fréchet spaces, sequential spaces, network, k-network, cs-network, $ {\aleph _0}$-spaces, sequence-covering mappings, quotient mappings, pseudo-open mappings, separable metric spaces, second countable spaces
Article copyright: © Copyright 1972 American Mathematical Society