| As an important research object of general topology,real line space and sorgenfrey line space has been providing endless examples and references for people to explore the property and structure of topological space.There are many similarities and differences between the two spaces in terms of topological structure and topological properties,which makes people begin to pay attention to the changes in the topological properties of transition space classes between them.Understanding the topological properties of these transition space classes is very helpful for exploring the relationship between the properties and structures of the topological space,as well as for constructing special topological spaces.This paper mainly does the following five aspects:Firstly,for(?)A(?)R,(R,τ_A)is local compact iff(R,τ_A)is a kω,-space,and also iff R\A is discrete and close in（R,τ_A,).Secondly，for(?)A(?)R,(R,τ_A)is zero-dimension space iff R\A is dense in(R,τ_A).Thirdly,for(?)A(?)R,(R,τ_A)is σ-compact iff R\A is countable and nowhere dense in(R,τ_A).Fourthly,for(?)A(?)R,(R,τ_A)(?)0 is always complete and subparacompact.Fifthly,if R\A is a Fσ-set in H-type space(R,τ_A),then(R,τ_A)is a quasi-metrizable space. |
