On Covering Homotopy Regular Morphism

In this paper, we define covering homotopy regular morphism in the homotopy category of pointed path-connected CW-spaces and discuss its existence conditions, properties and the close relationships to covering homotopy monomor-phism (epimorphism) and covering homotopy equivalence, and we also further discuss the week homotopy regular morphism's existence conditions, properties and the close relationships to week homotopy monomorphism (epimorphism) and week homotopy equivalence, which generalize some results of homeomorphic morphism, homotopy equivalence and homotopy regular morphism.In Chapter 1, we discuss the covering homotopy regular morphism. First, we introduce the concept of covering homotopy regular morphism in the homotopy category of pointed path-connected CW-spaces and discuss its existence conditions and properties. Second. we prove that Cartesian product preserves the properties of covering homotopy regular; Moreover, we further the conclusion on Smash product; At last we discuss the properties of covering homotopy regular preserve function space. In the last section of this chapter we introduce the concepts of (i,p)-covering homotopy inverse and covering group homotopy inverse respectively and discuss their existence conditions, properties and the close relationships to covering homotopy monomorphism (epimorphism) and covering homotopy equivalence, which generalize the results of covering homotopy regular morphism.In Chapter 2, we discuss the week homotopy regular morphism that is the generalization of covering homotopy regular morphism and discuss its properties and the close relationships to week homotopy monomorphism (epimorphism) and week homotopy equivalence. In the last section of this chapter we introduce the concepts of (i,p)-week homotopy inverse and week group homotopy inverse...