On i-topological spaces: generalization of the concept of a topological space via ideals

Irina Zvina


The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.


Compatible ideal; Generalization; Topological space

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1. Introduction to generalized topological spaces
Irina Zvina
Applied General Topology  vol: 12  issue: 1  year: 2013  
doi: 10.4995/agt.2011.1701

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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt