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

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- July 12th 2011, 02:37 AMstudent2011semi-metric spaces and qausi-semi developable
prove that every semi-metric space is qausi-semi developabel.

- July 12th 2011, 03:20 AMgirdavRe: semi-metric spaces and qausi-semi developable
Can you write the definitions of "semi-metric space" and "quasi-semi developable"? It's the first step to solve the problem.

- July 12th 2011, 10:54 AMstudent2011Re: semi-metric spaces and qausi-semi developable
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. - July 18th 2011, 01:38 AMstudent2011Re: semi-metric spaces and qausi-semi developable
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.