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TRANSITIVITY IN POINT-FREE TOPOLOGY

Part of: Boolean algebras (Boolean rings) Special categories Distributive lattices

Published online by Cambridge University Press:  29 June 2009

MOJGAN GOLZY
MOJGAN GOLZY*
Affiliation:
Department of Mathematics, Buffalo State College, 1300 Elmwood Avenue, 317 Bishop Hall, NY 14222, USA (email: [email protected])
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Abstract

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The main purpose of this paper is to develop a point-free notion of topological transitivity. First, we define transitive frame maps and transitive completely prime filters in Frm, the category of frames and frame maps. Then we discuss the relationship between these notions in Frm and the notions of topological transitive and transitive points in Top. Finally, we investigate the relationship between transitive frame maps and the existence of transitive completely prime filters.

Keywords

point-free topologyframetransitive frame maptopological transitivity

MSC classification

Secondary: 06D22: Frames, locales 18B30: Categories of topological spaces and continuous mappings 18B35: Preorders, orders and lattices (viewed as categories)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 317 - 323
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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