Symmetric \(g\)-functions
type: Item
instance of: scholarly article
title: Symmetric \(g\)-functions
zbMATH Open document ID: 1032.54015
DOI: 10.1016/S0166-8641(03)00102-0
author: Chris Good
author: Daniel Jennings
author: A. Mohamad
published in: Topology and its Applications
publication date: 2003-11-20T00:00:00Z
review text: Several classes of generalized metric spaces \((X,\tau)\) were characterized by \(g\)-functions \(g:\mathbb N \times X \rightarrow \tau\) such that \(x\in g(n,x)\) for each \(x\in X\) and each \(n\in \mathbb N\). The authors of this paper study the role of symmetric \(g\)-functions, i.e., such \(g\)-functions which satisfy \(x\in g(n,y)\) if and only if \(y\in g(n,x)\) for each \(n\in \mathbb N\) and all \(x,y \in X\). They identify and consider six classes of such functions, give relationships between them and explain their role in the theory of generalized metric spaces and especially in metrization theory.
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E30
zbMATH DE Number: 2006374
zbMATH Keywords: symmetric \(g\)-functions
zbMATH Keywords: metrizability
zbMATH Keywords: \(wM\)-space
zbMATH Keywords: \(o\)-semi-metrizable
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2006374