On continuity and generalized continuity with respect to two topologies
type: Item
instance of: scholarly article
title: On continuity and generalized continuity with respect to two topologies
zbMATH Open document ID: 0938.54020
published in: Real Analysis Exchange
publication date: 2000-05-21T00:00:00Z
review text: If \(\tau _1\) and \(\tau _2\) are two (not necessarily Hausdorff) topologies on \(X\) and \(\tau =\tau _1\cap \tau _2\), the relation of the continuity of a real-valued function \(f:X\to \mathbb R\) at an \(x\in X\) with respect to \(\tau \) to the continuity with respect to \(\tau _i\), \(i=1,2,\) is discussed. Similarly, the properties to be quasicontinuous at \(x\) and to be cliquish at \(x\) are also considered.
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 1449529
zbMATH Keywords: quasicontinuity
zbMATH Keywords: cliquishness
zbMATH Keywords: non-Hausdorff topologies
author: Zbigniew Grande
reviewed by: Petr Holický
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1449529