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April, 2002 Vietoris continuous selections on scattered spaces
Seiji FUJII, Kazumi MIYAZAKI, Tsugunori NOGURA
J. Math. Soc. Japan 54(2): 273-281 (April, 2002). DOI: 10.2969/jmsj/05420273


We prove that a countable regular space has a continuous selection if and only if it is scattered. Further we prove that a paracompact scattered space admits a continuous selection if each of its points has a countable pseudo-base. We also provide two examples to show that: (1) paracompactness can not be replaced by countable compactness even together with (collectionwise) normality, and (2) having countable pseudo-base at each of its points can not be omitted even in the class of regular Lindelöf linearly ordered spaces.


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Seiji FUJII. Kazumi MIYAZAKI. Tsugunori NOGURA. "Vietoris continuous selections on scattered spaces." J. Math. Soc. Japan 54 (2) 273 - 281, April, 2002.


Published: April, 2002
First available in Project Euclid: 9 June 2008

zbMATH: 1031.54024
MathSciNet: MR1883518
Digital Object Identifier: 10.2969/jmsj/05420273

Primary: 54C65
Secondary: 03E10 , 54B20

Keywords: (co-)stationary set , hereditarily Baire , hyperspace , ordered space , pressing down , scattered , selection

Rights: Copyright © 2002 Mathematical Society of Japan


Vol.54 • No. 2 • April, 2002
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