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Topic: Proximity space
Replies: 5   Last Post: Jun 16, 2013 9:39 PM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Proximity space
Posted: Jun 13, 2013 5:11 AM
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In Wikipedia's definition of proximity space,
axioms, definitions and theorems are given which are
hard to understand because of the strange charactes.

Here's what I've deciphered. How correct is it? A,B,C are subsets of S.
Writing AnB for "A near to B" or "A close to B", the axioms are:

AnB implies BnA
AnB implies A not empty
not emtpy A /\ B implies AnB
An(B \/ C) implies AnB or AnC

Then theorem for all C, (AnC or B~S\C) implies AnB

The deffinition A << B for not AnS\B
and the closure, cl A = { x | {x}nA }.

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