Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-28T14:55:39.167Z Has data issue: false hasContentIssue false

On the boundedness operator

Published online by Cambridge University Press:  17 April 2009

Panayotis Th. Lambrinos
Affiliation:
Department of Mathematics, University of Thessaloniki, Thessaloniki, Greece.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is a continuation of the study of the boundedness operator δ. By determination of the congruences (that is, collapsings) of the smallest lattice containing δ and closed under application of δ, a nev classification of all topological spaces is obtained according to boundedness criteria.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]de Groot, J., Herrlich, H., Strecker, G.E., Wattel, E., “Compactness as an operator”, Compositio Math. 21 (1969), 349375.Google Scholar
[2]Lambrinos, Panayotis, “A topological notion of boundedness”, Manuscripta Math. 10 (1973), 289296.CrossRefGoogle Scholar
[3]Λαμπρινου, Παναγιωτη Θ. [Panayotis Th. Lambrinos], “Τποσυνολα (m, n)-περατωμενα εισ τοπολογικον Χωρον” [(m, w)-bounded subsets of a topological space], (Doctoral Dissertation, University of Thessaloniki, Thessaloniki, Greece, 1974).Google Scholar
[4]Strecker, G.E., Wattel, E., Herrlich, H. and de Groot, J., “Strengthening Alexander's subbase theorem”, Duke Math. J. 35 (1968), 671676.CrossRefGoogle Scholar
[5]Wattel, E., The compactness operator in set theory and topology (Mathematical Centre Tracts, 21. Mathematisch Centrum, Amsterdam, 1968).Google Scholar