Quasicontinuous functions with values in Piotrowski spaces

TL;DR

This paper surveys properties of Piotrowski spaces, explores their relationships with other topological classes, and characterizes when such spaces contain dense metrizable Baire subspaces.

Contribution

It provides a comprehensive survey of Piotrowski spaces and establishes new equivalences involving dense metrizable Baire subspaces in these spaces.

Findings

Piotrowski spaces relate closely to fragmentable and Stegall spaces.

A Piotrowski Tychonoff space contains a dense metrizable Baire subspace iff it is Baire.

Characterization of Piotrowski spaces in terms of Baire and Choquet properties.

Abstract

A topological space $X$ is called 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).