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Topic: Any topology book that uses neighbourhood systems as starting point?
Replies: 3   Last Post: Aug 30, 2013 3:03 PM

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@less@ndro

Posts: 212
Registered: 12/13/04
Re: Any topology book that uses neighbourhood systems as starting point?
Posted: Aug 30, 2013 3:03 PM
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lookskywalker <LookSkywalker@gmail.com> wrote:
> Anyone know of (point set) topology books that define a topology on a
> set as a collection of neighbourhood systems?


I do not know any such book that *exclusively* defines a topology via
the axioms of neighbourhood systems without ever giving the axioms
of a system of open sets. Most books usually start with one or the other
axiom systems as the definition of a topology, and then show their
equivalence. After that it does not really matter which axiom system
was used in the beginning.

As far as I recall, the following two books start with the definition via
neighbourhoods:

Jameson: Topology and normed spaces
Brown: Topology and Groupoids

--
Marc



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