Re: 'Directed Algebraic Topology'

["George Janelidze" <janelg@telkomsa.net>]

Dear Colleagues,

In addition to my message of September 22 addressed to Michael Barr and all
of you (concerning 'Directed Algebraic Topology'/quasi-uniform spaces) I am
forwarding a message from Guillaume Brummer:

"...Thank you for copying this interesting material to me, and for
mentioning quasi-uniform spaces to Michael Barr. Serious early work in this
field was by Leopoldo Nachbin of Rio de Janeiro, published in CRASP 226
(1948) 774-775, -- just 11 years after Andre' Weil's monograph on uniform
spaces. Then came Nachbin's monograph Topologia e ordem (Chicago 1950), of
which an English translation Topology and order was published by Van
Nostrand (1964). Meantime the book by A'. Csa'sza'r, Fondements de la
topologie ge'ne'rale, had appeared in Paris (1960)..."

Guillaume Brummer also says:

"...Hans-Peter K"unzi has published several surveys of this field since
1993, with lots of bibliography..."

However, I still see no connection (which does not mean that it will never
occur!) between "directed/asymmetric algebraic topology" and "asymmetric
general topology". Surely Marco Grandis is the right person to ask about
this. Well, since Marco mentioned preordered topological spaces, one could
think of bitopological spaces and then quasi-uniform spaces might occur
naturally...

George Janelidze



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