Journal of the Mathematical Society of Japan

Vietoris continuous selections on scattered spaces

Seiji FUJII, Kazumi MIYAZAKI, and Tsugunori NOGURA

Full-text: Open access


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.

Article information

J. Math. Soc. Japan, Volume 54, Number 2 (2002), 273-281.

First available in Project Euclid: 9 June 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54C65: Selections [See also 28B20]
Secondary: 03E10: Ordinal and cardinal numbers 54B20: Hyperspaces

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


FUJII, Seiji; MIYAZAKI, Kazumi; NOGURA, Tsugunori. Vietoris continuous selections on scattered spaces. J. Math. Soc. Japan 54 (2002), no. 2, 273--281. doi:10.2969/jmsj/05420273.

Export citation