Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-07-03T23:15:26.681Z Has data issue: false hasContentIssue false
  • English
  • Français

Essential Extensions of T1-Spaces

Published online by Cambridge University Press:  20 November 2018

Rudolf-E. Hoffmann
Rudolf-E. Hoffmann*
Affiliation:
Fachbereich Mathematik, Universitaet Bremen D-2800 Bremen, Fed. Rep. of Germany
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.

In the category of T1 -spaces and continuous maps, every space X has a unique maximal essential extension. X has an injective hull iff card X≤1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 237 - 240
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Banaschewski, B., Essential extensions of T0-spaces. General Topology Appl.. 7 (1977), 233-246.Google Scholar
2. Banaschewski, B., Projective covers in categories of topological spaces and topological algebras. Proc. Kanpur Topology Conference, 1968. Academia, Prague, 1971.Google Scholar
3. Banaschewski, B., Injectivity and essential extensions in equational classes of algebras. Proc. Conference on Universal Algebra, Kingston 1969. Queen's University, Kingston, Ontario, 1970.Google Scholar
4. Borsuk, K., Theory of retracts. PWN (Polish Scientific Publishers), Warszawa, 1967.Google Scholar
5. Hoffmann, R.-E., Irreducible filters and sober spaces. Manuscripta Math.. 22 (1977), 365-380.Google Scholar
6. Hoffmann, R.-E., Essentially complete T0-spaces. Manuscripta Math.. 27 (1979) 401-432.Google Scholar
7. Thron, W. J., Lattice-equivalence of topological spaces. Duke Math. J.. 29 (1962), 671-679.Google Scholar