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tried to polish topological base a little.
I have added the concept of a subbase of topology and fundamental system of neighborhoods at a given point as well as mentioning the character of a topological space and separability axiom (first one, if my memory is right). Please check, I wrote quickly from my memory.
I made your
Definition
a
+-- {: .num_defn}
###### Definition
so that it appears in line with the rest.
I thought it was called the first axiom of countability. Doesn’t “separable” mean instead that there is a countable dense set of points?
Yes, Mike’s memory agrees with mine. I’ll edit it. Zoran, please complain if we are wrong.
This page should really just be about the concept in topological spaces, with a pointer to the much more extensive articles on bases for Grothendieck topologies. I am going to boldly change this too. Urs, please complain.
Urs, please complain.
No, why? Go ahead.
Good!
Yes, the first axiom of countability. I mistranslated to English, coupled with weak memory :) The page looks quite good after all your interventions !
I’m glad that everybody is happy!
Ironically, separability got into the page anyway, in the example showing the base that proves that separable metric spaces are second-countable.
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