International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 823-825

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

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.


M. K. Singal and Asha Rani Singal have defined an almost-continuous function f:XY to be one in which for each xX 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,y1Y there exists an almost-continuous f:IY 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.