Almost-continuous path connected spaces

[摘要] M. K. Singal and Asha Rani Singal have defined an almost-continuousfunctionf:X→Yto be one in which for eachx∈Xand each regular-open setVcontainingf(x), there exists an openUcontainingxsuch thatf(U)⊂V. A spaceYmay now be defined to be almost-continuous path connected if for eachy0,y1∈Ythere exists an almost-continuousf:I→Ysuch thatf(0)=y0andf(1)=y1An investigation of these spaces is made culminating in a theorem showing when thealmost-continuous path connected components coincide with the usual components ofY.

[学科分类] 数学（综合）