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




Proximity space
Posted:
Jun 13, 2013 5:11 AM


In Wikipedia's definition of proximity space, http://en.wikipedia.org/wiki/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 }.



