International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 823-826
doi:10.1155/S0161171281000641
Almost-continuous path connected spaces
Larry L. Herrington1
and Paul E. Long2
1Department of Mathematics, Louisiana State University at Alexandria, Alexandria 71402, Louisiana, USA
2Department of Mathematics, The University of Arkansas at Fayetteville, Fayetteville 72701, Arkansas, USA
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.