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