Almost-continuous path connected spaces

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 y0,y1∈Y there exists an almost-continuous f:I→Y such that f(0)=y0 and f(1)=y1 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.