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.