D. Cantone et V. Cutello, DECISION ALGORITHMS FOR ELEMENTARY TOPOLOGY .1. TOPOLOGICAL SYLLOGISTICS WITH SET AND MAP CONSTRUCTS, CONNECTEDNESS, AND CARDINALITY COMPARISON, Communications on pure and applied mathematics, 47(9), 1994, pp. 1197-1217
In this paper we give a decision procedure for a topological syllogist
ic, denoted L2,infinity, involving, besides the standard Boolean set o
perators (or, and, \, ' (set complementation)) and predicates (is-an-e
lement-of (membership), = (equality)), also the Kuratowski closure ope
rator , continuous and closed maps with the notion of direct and inver
se images, surjectivity and injectivity, as well as point evaluation,
the singleton operator {.}, a predicate for comparing the cardinalitie
s of two given sets, and a predicate expressing that a given set is to
pologically connected. Several examples are also discussed. (C) 1994 J
ohn Wiley & Sons, Inc.