Almost-continuous path connected spaces

Larry L. Herrington and Paul E. Long

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-3

Abstract:

M. K. Singal and Asha Rani Singal have defined an almost-continuous function f : X → Y to be one in which for each x ∈ X and each regular-open set V containing f ( x ) , there exists an open U containing x such that f ( U ) ⊂ V . A space Y may now be defined to be almost-continuous path connected if for each y 0 , y 1 ∈ Y there exists an almost-continuous f : I → Y such that f ( 0 ) = y 0 and f ( 1 ) = y 1 An investigation of these spaces is made culminating in a theorem showing when the almost-continuous path connected components coincide with the usual components of Y .

Date: 1981
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DOI: 10.1155/S0161171281000641

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