A Baues fibration category of P-spaces

The article is concerned with homotopy in the category P whose objects are the pairs (X, *) consisting of a Polish space X and a closed binary operation *. Homomorphisms in P are continuous maps compatible with the operations. The result showed that the category P admits the structure of a fibration category in the sense of H. Baues. The notions of fibration and weak equivalence are defined in the category P and showed to satisfy fundamental properties that the corresponding notions satisfy in the category Top of topological spaces. (C) 2016 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.