2016/02/23 by Pop, Ioan
#54E99 #55P99 #55R05 #55R65 #55U35 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1602.07105
In a previous paper [21] the author studied the homotopy lifting property in the category dTop of directed spaces in the sense of M. Grandis [12], [13], [14]. The present paper, which is a continuation of aforementioned article, introduces and studies the directed weak homotopy property (dWCHP) and directed weak fibrations, extending to the category dTop the well known Dold's (or weak) - fibrations [6]. The dWCHP is characterized in several ways. Then the notion of a directed fibre homotopy equivalence (dFHE) between directed weak fibrations is studied. Some examples and counterexamples are given.