Local Connectedness Of Extension Spaces

Bernhard Banaschewski

doi:10.4153/CJM-1956-044-8

Extract

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.

1. Introduction. An extension E* of a topological space E (that is, a space containing E as a dense subspace) determines a family of filters (u) on E, given by the traces U ∩ E of the neighbourhoods U ⊆ E* of each u ∈ E* − E. Many topological properties of an extension E* of a given space E can be related to properties of these trace filters (as we shall call them) belonging to E*.

References

1. Alexandroff, P., Bikompakte Erweiterung topologischer Räurne, Mat. Sbornik, N.S., 5 (1939), 420–428.Google Scholar

2. Banaschewski, B., Ueberlagerungen von Erweiterungsräumen, to appear in Archiv der Mathematik.Google Scholar

3. Bourbaki, N., Topologie générale (Act. sci. industr., Paris).Google Scholar

4. Katětov, M., Über H-abgeschlossene und bikompakte Ràunie, Časopis Mat. Fys., 69 (1939-40), 36–49.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Stephenson, R. M. 1968. Pseudocompact spaces. Transactions of the American Mathematical Society, Vol. 134, Issue. 3, p. 437.

Wulbert, Daniel E. 1969. A characterization of 𝐶(𝑋) for locally connected 𝑋. Proceedings of the American Mathematical Society, Vol. 21, Issue. 2, p. 269.

Hursch, J.L. 1971. The local connectedness of ga compactifications generated by all closed connected sets. Indagationes Mathematicae (Proceedings), Vol. 74, Issue. , p. 411.

Kohli, J. K. 1978. A Class of Spaces Containing all Connected and all Locally Connected Spaces. Mathematische Nachrichten, Vol. 82, Issue. 1, p. 121.

Hartig, Donald G. 1978. Local connectedness and pseudocompactness in completely regular spaces. Proceedings of the American Mathematical Society, Vol. 68, Issue. 1, p. 117.

Tinkler, Keith J. 1979. Graph theory. Progress in Human Geography, Vol. 3, Issue. 1, p. 85.

1985. Modern General Topology. Vol. 33, Issue. , p. 496.

Baboolal, D. 1991. Locally connected compactifications. Topology and its Applications, Vol. 40, Issue. 1, p. 23.

Baboolal, D. and Banaschewski, B. 1991. Compactification and local connectedness of frames. Journal of Pure and Applied Algebra, Vol. 70, Issue. 1-2, p. 3.

BANASCHEWSKI, B. 1992. Recent Results in Pointfree Topology. Annals of the New York Academy of Sciences, Vol. 659, Issue. 1, p. 29.

Chen, Xiangdong 1992. On the local connectedness of frames. Journal of Pure and Applied Algebra, Vol. 79, Issue. 1, p. 35.

Henriksen, Melvin 1997. Handbook of the History of General Topology. Vol. 1, Issue. , p. 243.

Baboolal, D. 2000. Papers in Honour of Bernhard Banaschewski. p. 377.

Hoshina, Takao 2003. Encyclopedia of General Topology. p. 65.

Farhadi, M. and Koushesh, M.R. 2017. A Gelfand–Naimark type theorem. Topology and its Applications, Vol. 228, Issue. , p. 145.

Bogachev, V. I. 2024. Compactification of Spaces of Measures and Pseudocompactness. Doklady Mathematics,

Article contents

Local Connectedness Of Extension Spaces

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests