Regular weakly homotopy and Regular weakly homotopy type spaces

Abstract

In this paper, we introduce the term of regular weakly homotopy (briefly, $rw$-homotopy) of $rw$-continuous maps, $rw$-homotopy equivalence classes,same $rw$-homotopy type, $rw$-contractible spaces, and certain notions in irresolute homotopy. We obtain fundamental properties and few consequences of respective notions including results on relative homotopy as well presurvness of such homotopy under compositions. Also, we present the Induced maps and their properties, and consequences with respect to some notions.