Thread: semi-metric spaces and qausi-semi developable

prove that every semi-metric space is qausi-semi developabel.

Can you write the definitions of "semi-metric space" and "quasi-semi developable"? It's the first step to solve the problem.

I know the definition of both semi-metric spaces and qausi-semi developable spaces. A space X is called a semi-metric space if there is a distance function such that:
1)
2) iff
3) iff is a limit point of

A topological space is said to be a qausi-semi developable if there exist a sequence of subsets of such that for each and each open set containing there exists an n with is contained in .

So in order to prove that every semi-metric space is a qausi-semi developable space, we should get the a qausi-semi development. How can I get it, please guide me.

Ok, thank you very much, I got the answer, in fact every semimetrizable spaces are semi-developable and thus qausi-semi developable.

I attached the answer in the attachement.