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 | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Fréchet 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