Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-17T02:46:21.923Z Has data issue: false hasContentIssue false

Solid convergence spaces

Published online by Cambridge University Press:  17 April 2009

M. Schroder
Affiliation:
Department of Mathematics, University of Waikato, Hamillton, New Zealand.
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.

The category of solid convergence spaces is introduced, and shown to lie strictly between the category of all convergence spaces and that of pseudo-topological spaces. A wide class of convergence spaces, including the c-embedded spaces of Binz, is then characterized in terms of this concept. Finally, several illustrative examples are given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Binz, E., “Bemerkungen zu limitierten Funktionenalgebren”, Math. Ann. 175 (1968), 169184.CrossRefGoogle Scholar
[2]Binz, E., “Kompakte Limesräume and limitierte Funktionenalgebren”, Comment. Math. Helv. 43 (1968), 195203.CrossRefGoogle Scholar
[3]Binz, E. and Keller, H.H., “Funktionenräume in der Kategorie der Limesräume”, Ann. Acad. Soi. Fenn. Ser. AI 383 (1966).Google Scholar
[4]Fischer, H.R., “Limesräume”, Math. Ann. 137 (1959), 269303.CrossRefGoogle Scholar
[5]Hewitt, Edwin, “On two problems of Urysohn”, Ann. of Math. 47 (1946), 503509.CrossRefGoogle Scholar
[6]Müller, B., “L c - und C-einbettbare Limesräume”, Preprint (Universität Mannheim, 1972).Google Scholar