Introduction to generalized topological spaces

Authors

  • Irina Zvina University of Latvia

DOI:

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

Keywords:

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

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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Author Biography

Irina Zvina, University of Latvia

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

References

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How to Cite

[1]
I. Zvina, “Introduction to generalized topological spaces”, Appl. Gen. Topol., vol. 12, no. 1, pp. 49–66, Apr. 2011.

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