Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T11:00:01.407Z Has data issue: false hasContentIssue false
  • English
  • Français

On almost locally connected spaces

Part of: Maps and general types of spaces defined by maps Fairly general properties

Published online by Cambridge University Press:  09 April 2009

Takashi Noiri
Takashi Noiri
Affiliation:
Department of Mathematics Yatsushiro College of TechnologyYatsushiro-shi, Kumamoto-ken 866, Japan
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 this paper it is shown that aimost local connectedness is hereditary for the subspace that is the union of regular open sets and is preserved under almost-open (in the sense of Singal) θ-continuous surjections.

MSC classification

Secondary: 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54D05: Connected and locally connected spaces (general aspects)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 258 - 264
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Fomin, S., ‘Extensions of topological spaces’, Ann. of Math. 44 (1943), 471–480.CrossRefGoogle Scholar
[2]Levine, N., ‘A decomposition of continuity in topological spaces’, Amer. Math. Monthly 68 (1961), 44–46.CrossRefGoogle Scholar
[3]Mancuso, V. J., ‘Almost locally connected spaces’, J. Austral. Math. Soc. Ser. A 31 (1981), 421–428.CrossRefGoogle Scholar
[4]Noiri, T., ‘On weakly continuous mappings’, Proc. A mer. Math. Soc. 46 (1974), 120–124.CrossRefGoogle Scholar
[5]Noiri, T., ‘On δ-continuous functions’, J. Korean Math. Soc. 16 (1980), 161–166.Google Scholar
[6]Noiri, T., ‘A note on η-continuous functions’, J. Korean Math. Soc. 18 (1981), 37–42.Google Scholar
[7]Noiri, T., ‘Semi-continuity and weak-continuity’, Czechoslovak. Math. J. 31 (1981), 314–321.CrossRefGoogle Scholar
[8]Pervin, W. J. and Levine, N., ‘Connected mappings of Hausdorff spaces’, Proc. Amer. Math. Soc. 9 (1958), 488–495.CrossRefGoogle Scholar
[9]Porter, J. and Thomas, J., ‘On H-closed and minimal Hausdorff spaces’, Trans. Amer. Math. Soc. 138 (1969), 159–170.Google Scholar
[10]Rose, D. A., ‘Weak continuity and almost continuity’, preprint.Google Scholar
[11]Singal, M. K. and Mathur, Asha, ‘On nearly-compact spaces’, Boll. Un. Mat. Ital. (4) 2 (1969), 702–710.Google Scholar
[12]Singal, M. K. and Singal, A. R., ‘Almost-continuous mappings’, Yokohama Math. J. 16 (1968), 63–73.Google Scholar
[13]Soundararajan, T., ‘Weakly Hausdorff spaces and the cardinality of topological spaces’, General topology and its relations to modern analysis and algebra III, Proc. Conf. Kampur, 1968, pp. 301–306 (Academia, Prague, 1971).Google Scholar