Open Access
April, 2014 Hausdorff continuous sections
Valentin GUTEV
J. Math. Soc. Japan 66(2): 523-534 (April, 2014). DOI: 10.2969/jmsj/06620523


It is shown that a space $X$ is strongly paracompact if and only if for every complete metric space $(Y,\rho)$, every l.s.c. mapping from $X$ into the nonempty closed subsets of $Y$ has a separable-valued Hausdorff continuous section. Several applications are demonstrated as well.


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Valentin GUTEV. "Hausdorff continuous sections." J. Math. Soc. Japan 66 (2) 523 - 534, April, 2014.


Published: April, 2014
First available in Project Euclid: 23 April 2014

zbMATH: 1297.54041
MathSciNet: MR3201824
Digital Object Identifier: 10.2969/jmsj/06620523

Primary: ‎54C60‎ , 54C65
Secondary: 54B20 , 54D20

Keywords: branch , Hausdorff continuous , lower semi-continuous , section , set-valued mapping , strong paracompactness , tree , upper semi-continuous

Rights: Copyright © 2014 Mathematical Society of Japan

Vol.66 • No. 2 • April, 2014
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