Note on limits of simply continuous and cliquish functions
type: Item
instance of: scholarly article
title: Note on limits of simply continuous and cliquish functions
zbMATH Open document ID: 0799.54011
DOI: 10.1155/S0161171294000645
author: Janina Ewert
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1994-10-09T00:00:00Z
full work available at URL: https://eudml.org/doc/47010
review text: Summary: The main result of this paper is that any function \(f\) defined on a perfect Baire space \((X,T)\) with values in a separable metric space \(Y\) is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence \(\{f_ n : n \geq 1\}\) of simply continuous functions. This result is obtained by a change of a topology on \(X\) and showing that a function \(f:(X,T) \to Y\) is cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 26A21
zbMATH DE Number: 650812
zbMATH Keywords: simple continuity
zbMATH Keywords: cliquishness
zbMATH Keywords: function with the Baire property
zbMATH Keywords: perfect Baire space
MaRDI profile type: Publication
OpenAlex ID: W1985491120
description: scientific article; zbMATH DE number 650812