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Cech closure spaces.

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dc.contributor.author Roth, David N.
dc.date.accessioned 2012-12-13T15:51:37Z
dc.date.available 2012-12-13T15:51:37Z
dc.date.created 1979 en_US
dc.date.issued 2012-12-13
dc.identifier.uri http://hdl.handle.net/123456789/2287
dc.description 24, [1] leaves en_US
dc.description.abstract This paper presents an introduction to Cech closure spaces. The set of all Cech closure operators on a set is closed under the operations of union and composition. An association between Cech closure operators on a finite set and zero-one relation matrices is used to present matrix operations corresponding to union and composition of Cech closure operators. Finitely generated Cech closure operators are defined, and it is shown that the set of all finitely generated Cech closure operators on a set, partially ordered in a natural way, yields a uniquely complemented, distributive, and complete lattice and is therefore a Boolean algebra. A Cech closure operator generates a semi-topology and an underlying topology; relationships between these are studied. Several separation properties are generalized to Cech closure spaces and studied in this broader context. en_US
dc.language.iso en_US en_US
dc.subject Closure operators. en_US
dc.subject Algebra, Boolean. en_US
dc.title Cech closure spaces. en_US
dc.type Thesis en_US
dc.college las en_US
dc.advisor John W. Carlson en_US
dc.department mathematics, computer science, and economics en_US

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