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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0300253-7
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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Keywords: Fr&#233;chet spaces, sequential spaces, network, <I>k</I>-network, <I>cs</I>-network, <!– MATH ${\aleph _0}$ –> <IMG WIDTH="27" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="${\aleph _0}$">-spaces, sequence-covering mappings, quotient mappings, pseudo-open mappings, separable metric spaces, second countable spaces
Article copyright: © Copyright 1972 American Mathematical Society