There are many documents, describing or characterizing separation axioms, both "classical", like T0, T1, T2, and others, defined using more complicated conditions. Is there any document, registering the origin and evolution of those mathematical concepts, characterizing topological spaces, or anybody has that knowledge and can share it?
Dear Rey Segundo Guerrero-Proenza
You can find some of them with some properties in the attached file.
Dear Rey Segundo Guerrero-Proenza ,
The following websites and the references therein are rich in information about the history of separation axioms:
mathworld.wolfram.com › Topology › Point-Set Topology
https://en.wikipedia.org › wiki › History_of_the_separation_axioms
https://en.wikipedia.org › wiki › Separation_axiom
Best regards
Dear Dr. Kaddoura,
Thank you, I am deeply grateful for your contribution.
Best regards,
Dear Guerrero-Proenza,
See also the books of Murdeshwar, Naimpally, Fletcher and Lindgren
on Quasi-Uniform Spaces.
Separation axioms and many other topological properties can be most nicely treated in Relator Spaces.
A Relator Space is a pair (X, Y)(Cal R) = ((X, Y), Cal R) consisting of
two sets X and Y and a family Cal R of relations R on X to Y.
Relator Spaces have been mainly studied by me and my very few
followers.
They are still completely neglected by topologists and
the editors of the Math. Subject Classifications.
With best regards,
Arpad Szaz
See the following website,
https://ncatlab.org/nlab/show/separation+axioms
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