Relations and topologies
نویسندگان
چکیده
منابع مشابه
Transitive Relations, Topologies and Partial Orders
Let be a set with elements. A subset of × is a binary relation (or relation) on . The number of relations on is 22. Equivalently, there are 2 2 labeled bipartite graphs on 2 vertices, assuming the bipartition is fixed and equitable. A relation on is reflexive if for all ∈ , we have ( ) ∈ . The number of reflexive relations on is 2(−1). A relation on is antisymm...
متن کاملCovering Relations in the Lattice of ^-topologies
A topology ^"i is said to cover another topology T3 if ^Ç^i and no other topology may be included between the two. In this paper, we characterize the relationship between a Tj-topology and its covers. This characterization is used to prove that the lattice of 7\-topologies is both upper and lower semimodular. We also prove that the sublattice generated by the covers of a 7\-topology is isomorph...
متن کاملTopologies Induced by Relations with Applications
Some methods for inducing topological structures by relations were initiated and their importance in applications were indicated. Topologies generated by equivalence relations were all quasi-discrete spaces. We induced the topologies generated using similarity relations and pre-order relations. Also, the topologies generated using general binary relations on the universe of discourse were initi...
متن کاملOn topologies generated by Moisil resemblance relations
In [8] and [9] Moisil has introduced the resemblance relations. Following [9] we associate to every resemblance relation an extensive operator which commutes with arbitrary unions of sets. We are leading to consider spaces endowed with such closure operators; we shall call these spaces total tech spaces (TC-spaces). TC-spaces are in one-to-one, onto correspondence with reflexive relations. TC-s...
متن کاملn-Tuple relations and topologies on function spaces
In [7] some results concerning S-splitting, S-jointly continuous, D-splitting and D-jointly continuous topologies are considered, where S and D are the Sierpinski space and the double-point space, respectively. Here we generalize these results replacing the spaces S and D by any finite space. 2000 AMS Classification: 54C35.
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1993
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1993.128381