Directed weak and directed Dold fibrations
Received: 4.V.2017, Accepted: 14.III.2018
Abstract. In a previous paper  the author studied the homotopy lifting property in the category dTop of directed spaces in the sense of M. Grandis , , . The present paper, which is a continuation of the aforementioned article, introduces and studies the directed weak homotopy property (dWCHP) and directed covering semistationary homotopy property (dCSHP) defining directed weak fibrations and directed Dold fibrations respectively, both extending to the category dTop the well known Dold’s  (or weak ) fibrations, but which are not equivalent as in the undirected case. Then the notion of a directed fibre homotopy equivalence (dFHE) between directed Dold fibrations is studied. Some examples and counterexamples are given.
Mathematics Subject Classification (2010): 55R05, 55P99, 55U35, 55R65, 54E99
I. Pop, Faculty of Mathematics, “Al. I. Cuza” University, 700505-Iaşi, România