International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 823-825
doi:10.1155/S0161171281000641
Almost-continuous path connected spaces
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
Received 31 October 1980
Copyright © 1981 Larry L. Herrington and Paul E. Long. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.