Weakly α -continuous functions

Takashi Noiri

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-8

Abstract:

In this paper, we introduce the notion of weakly α -continuous functions in topological spaces. Weak α -continuity and subweak continuity due to Rose [1] are independent of each other and are implied by weak continuity due to Levine [2]. It is shown that weakly α -continuous surjections preserve connected spaces and that weakly α -continuous functions into regular spaces are continuous. Corollary 1 of [3] and Corollary 2 of [4] are improved as follows: If f 1 : X → Y is a semi continuous function into a Hausdorff space Y , f 2 : X → Y is either weakly α -continuous or subweakly continuous, and f 1 = f 2 on a dense subset of X , then f 1 = f 2 on X .

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:637261

DOI: 10.1155/S0161171287000565

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