Kuratowski K., Introduction to Set Theory and Topology, PWN, Warsaw, 1977. Home/Search Document Not in Database Summary Related Articles Check |
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Representing Geometries Of Geographic Space - Bittner, Frank (Correct)
....used to model the extent of spatial phenomena, e.g. sets of points in the plane which members are arbitrarily scattered. In order to model the extent of spatial phenomena one needs a notion of neighborhood. Point set topology is the study of subsets of a point set using the notion of neighborhood (Kuratowski 1962). Open and closed sets are distinguished in terms of neighborhood. Intuitively, closed sets are sets representing regions with their boundary. Regular closed sets (Requicha 1977) are closed sets that represent regions which boundaries are well shaped . Regular closed sets of a 2D space are used ....
Kuratowski, K. (1962). Introduction to Set Theory and Topology. Oxford, Pergamon Press LTD.
Carving Up Space: steps towards construction of an absolutely.. - Bennett (8 citations) (Correct)
....that that there are n 1 mutually equidistant points and no more than that. Topologically a space is said to be of dimension n, if every open cover fO 1 ; O k g can be refined to a closed cover fC 1 ; C k g, such that every point in U occurs in at most n 1 of the C i s (Kuratowski 1972). For example, if a 2D region is covered by overlapping open patches then the region can always be covered by non overlapping closed regions, such that each is a part of one of the regions in the original open cover and no point is shared by more than three regions. Because it involves ....
Kuratowski, K.: 1972, Introduction to Set Theory and Topology, 2nd edn, Pergamon Press.
Neighborhood Expansion Grammars - Pfaltz (1999) (Correct)
....structure of a discrete system. Neighborhood expansions have been defined so as to homomorphically preserve this concept of structure. Any closure operator must satsify the axioms: X X: X Y implies X: Y: and X: X: where X;Y U are arbitrary subsets in a universe U of interest [12]. If in addition, X: Y: implies (X Y ) X: we say that is uniquely generated. For example, monophonic closure [6] in which X: denotes all points lying on chordless paths between distinct points p; q 2 X is uniquely generated over chordal graphs. A vector space, or matroid M, is the ....
Kazimierz Kuratowski. Introduction to Set Theory and Topology. Pergamon Press, 1972.
Fundamenta Informaticae 68 (2005) 47--102 47 IOS Press - Calculus Of Bounded (Correct)
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Kuratowski K., Introduction to Set Theory and Topology, PWN, Warsaw, 1977.
The Role of Completeness in Convergence of - Evolutionary Algorithms Eugene (Correct)
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Kuratowski K., Introduction to Set Theory and Topology, PWN, Warsaw, 1977.
BioSystems 82 (2005) 1--19 - Toward Theory Of (Correct)
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Kuratowski, K., 1977. Introduction to Set Theory and Topology. PWN, Warsaw.
Spatial Reasoning with Propositional Logics - Bennett (1994) (49 citations) (Correct)
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Kuratowski, K. Introduction to Set Theory and Topology, 2nd ed. Pergamon Press, 1972.
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