Introduction to generalized topological spaces

Irina Zvina

Latvia

University of Latvia

Department of Mathematics, Zellu str. 8, LV-1002, Riga, Latvia.

Submitted: 2013-09-16

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Accepted: 2013-09-16

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DOI: https://doi.org/10.4995/agt.2011.1701
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Keywords:

Generalized topology, Generalized topological space, gt-space, Compatible ideal, Modulo ideal, Frame, Order generated by ideal

Supporting agencies:

This research was not funded

Abstract:

We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
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