Real Analysis Exchange

Quasicontinuous functions with values in Piotrowski spaces

Taras Banakh

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Abstract

A topological space \(X\) is called {\em Piotrowski} if every quasicontinuous map \(f:Z\to X\) from a Baire space \(Z\) to \(X\) has a continuity point. In this paper we survey known results on Piotrowski spaces and investigate the relation of Piotrowski spaces to strictly fragmentable, Stegall, and game determined spaces. Also we prove that a Piotrowski Tychonoff space \(X\) contains a dense (completely) metrizable Baire subspace if and only if \(X\) is Baire (Choquet).

Article information

Source
Real Anal. Exchange, Volume 43, Number 1 (2018), 77-104.

Dates
First available in Project Euclid: 2 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1525226425

Digital Object Identifier
doi:10.14321/realanalexch.43.1.0077

Mathematical Reviews number (MathSciNet)
MR3816434

Zentralblatt MATH identifier
06924876

Subjects
Primary: 54C08: Weak and generalized continuity 54E35: Metric spaces, metrizability 54E35: Metric spaces, metrizability
Secondary: 54E18: $p$-spaces, $M$-spaces, $\sigma$-spaces, etc.

Keywords
quasicontinuous function minimal usco map Piotrowski space Stegall space

Citation

Banakh, Taras. Quasicontinuous functions with values in Piotrowski spaces. Real Anal. Exchange 43 (2018), no. 1, 77--104. doi:10.14321/realanalexch.43.1.0077. https://projecteuclid.org/euclid.rae/1525226425


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