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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 3rd 2012

tried to polish topological base a little.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeSep 5th 2012
• (edited Sep 5th 2012)

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeSep 5th 2012
• (edited Sep 5th 2012)

   Definition


a

 +-- {: .num_defn}
###### Definition


so that it appears in line with the rest.

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeSep 5th 2012
• (edited Sep 5th 2012)

I thought it was called the first axiom of countability. Doesn’t “separable” mean instead that there is a countable dense set of points?

• CommentRowNumber5.
• CommentAuthorTobyBartels
• CommentTimeSep 6th 2012
• (edited Sep 6th 2012)

Yes, Mike’s memory agrees with mine. I’ll edit it. Zoran, please complain if we are wrong.

• CommentRowNumber6.
• CommentAuthorTobyBartels
• CommentTimeSep 6th 2012

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.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeSep 6th 2012

• CommentRowNumber8.
• CommentAuthorTobyBartels
• CommentTimeSep 7th 2012

Good!

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeSep 7th 2012

Yes, the first axiom of countability. I mistranslated to English, coupled with weak memory :) The page looks quite good after all your interventions !

• CommentRowNumber10.
• CommentAuthorTobyBartels
• CommentTimeSep 7th 2012

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.

• CommentRowNumber11.
• CommentAuthorVitalyR
• CommentTimeApr 8th 2020

This change adds one more redirect.