Real Analysis Exchange

Quasicontinuous functions with values in Piotrowski spaces

Taras Banakh

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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

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

First available in Project Euclid: 2 May 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

quasicontinuous function minimal usco map Piotrowski space Stegall space


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.

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