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Almost locally connected spaces

Part of: Fairly general properties Peculiar spaces

Published online by Cambridge University Press:  09 April 2009

Vincent J. Mancuso
Vincent J. Mancuso
Affiliation:
Department of Mathematics, St. John's University, Jamaica, New York 11439, U.S.A.
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Abstract

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This paper introduces the concept of an almost locally connected space. Every locally connected space is almost locally connected, and the concepts are equivalent in the class of semi-regular spaces. Almost local connectedness is hereditary for regular open subspaces, is preserved by continuous open maps, but not generally by quotient maps. It is productive in the presence of almost-regularity.

Keywords

Almost locally connectedlocally connectedregular openalmost continuousalmost regular

MSC classification

Secondary: 54D05: Connected and locally connected spaces (general aspects) 54G10: $P$-spaces 54D10: Lower separation axioms ($T_0$--$T_3$, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 421 - 428
Copyright
Copyright © Australian Mathematical Society 1981

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