Bennett, B. A categorical axiomatisation of region-based geometry. Fundamenta Informaticae 46(1-2) (2001), 145-158. Home/Search Document Details and Download
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Space, Time, Matter and Things - Bennett Self-citation (Bennett) (Correct)
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BENNETT, B. A categorical axiomatisation of region-based geometry. Fundamenta Informaticae 46, 1--2 (2001), 145--158.
A Proximity Approach to Some Region-Based Theories of.. - Vakarelov, Dimov.. (2002) Self-citation (Bennett) (Correct)
....notions of the theory. Besides the early work of Tarski [38] and Leonard and Goodman [26] other papers related to Whitehedian region based approach to the theory of space include Grzegorczyk [20] Clarke [7, 8] Biacino and Gerla [3, 4] Roeper [31] Morroann [28] Bennett et al. 2] and Bennett [1]. We refer to the paper of Gerla [19] for a good survey on pointless geometry. The fact that mereological relations such as part of , overlap , non tangen tial inclusion and others can be defined in terms of the connection relation relates some pointless geometries to the field of mereology ....
....and, for A,B C X, define ASB iff d(A,B) O, whered(A,B) inf d(x,y) x E A,y B . Then5 is an Efremovi proximity on the space (X, d) 9 5. Let (X, be a completely regular space. Recall that two subsets A, B of X are completely separated iff there is a continuous real valued function f: X [0,1] such that f(A) 0 and f(B) 1. We can define a basic proximity 5 on X, satisfying the axiom (EF) by A( 5)B iff A and B are completely separated. Fact 3.5 (see, e.g. 29] If (X, is a compact Hausdorff space, then it admits a unique Efremovi proximity 5, namely the standard one. Fact ....
BENNETT, B. A categorical axiomatisation of region-based geometry. Fundamenta Informaticae 36(1-2) (2001), 145 158.
A Proximity Approach to Some Region-Based Theories of.. - Vakarelov, Dimov.. (2002) (Correct)
No context found.
Bennett, B. A categorical axiomatisation of region-based geometry. Fundamenta Informaticae 46(1-2) (2001), 145-158.
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