Inverse and symmetric relators
type: Item
instance of: scholarly article
title: Inverse and symmetric relators
zbMATH Open document ID: 0769.54028
DOI: 10.1007/BF00051766
published in: Acta Mathematica Hungarica
publication date: 1993-04-01T00:00:00Z
review text: The author provides more of the basic calculus of relators --- see (the reviews of) the papers of the author [ibid. 50, 177-201 (1987; Zbl 0643.54033)] and of \textit{J. Mala}, ibid. 60, 291-297 (1992; see review 54026 above)]. This paper connects (i) the `topological ideas' defined by a relator \(\mathcal R\) (such as the limit and adherence sets of nets, the closures and interiors of sets, and open and closed sets), (ii) various modifications of \(\mathcal R\) (in particular, its uniform, proximal and topological modifications), (ii) the inverses of \(\mathcal R\) and of these modifications, and (iv) various symmetry properties of \(\mathcal R\), linked to the modifications in (ii). Throughout, the regularity/symmetry axiom \(R_ 0\) lies close at hand, and the ideas of \textit{A. S. Davis} [Am. Math. Mon. 68, 886-894 (1961; Zbl 0106.155)] and \textit{W. J. Pervin} [Math. Ann. 147, 316-317 (1962; Zbl 0101.405)] provide examples and augment the theory. (As this paper shows, relator theory can use terminology from other general approaches to uniformity. The mathematical community now needs a formal comparison with these approaches --- its advantages, its weaknesses, its ease of use... and above all, its completion theory).
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 149628
zbMATH Keywords: relator
zbMATH Keywords: reflexive relation
zbMATH Keywords: symmetric relation
zbMATH Keywords: inverse relation
author: Árpád Száz
MaRDI profile type: Publication
cites work: Proximities, screens, merotopies, uniformities. I. II
cites work: Q5589071
cites work: Indexed Systems of Neighborhoods for General Topological Spaces
cites work: Q4045300
cites work: Q3966761
cites work: On spaces which are essentially T1
cites work: Two Theorems About Relations
cites work: On uniform topologies in general spaces
cites work: Q3228113
cites work: Q4162178
cites work: Q5616670
cites work: Q4403453
cites work: On Topologically Induced Generalized Proximity Relations
cites work: Q4271453
cites work: Q5515104
cites work: Q5536108
cites work: Connector theory
cites work: Q4180760
cites work: Quasi-uniformization of topological spaces
cites work: Q5837890
cites work: Q3481976
cites work: Basic tools and mild continuities in relator spaces
cites work: Q3468278
cites work: Projective and inductive generations of relator spaces
cites work: Q3658720
full work available at URL: https://doi.org/10.1007/bf00051766
OpenAlex ID: W2016381989
Recommended article: Q4826012
Recommended article: Inverse relations and Schauder bases
Recommended article: Q3199120
Recommended article: Symmetric and Isometric Relations
Recommended article: Q4849745
Recommended article: Q3611746
Recommended article: Involution and symmetry reductions
Recommended article: Inverse Conjugacies and Reversing Symmetry Groups
Recommended article: Q4207158
Recommended article: Q4716824
description: scientific article; zbMATH DE number 149628