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


  • Irina Zvina University of Latvia




Compatible ideal, Generalization, Topological space


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.


Download data is not yet available.

Author Biography

Irina Zvina, University of Latvia

Institute of Mathematics of Latvian Academy of Sciences


F. G.Arenas, J.Dontchev, M. L.Puertas, Idealization of some weak separation axioms, Acta Math. Hung. 89 (1-2) (2000), 47–53. http://dx.doi.org/10.1023/A:1026773308067

R.Engelking, General Topology, Warszawa, 1977.

T. R.Hamlett and D. Jankovic, Ideals in Topological Spaces and the Set Operator , Bollettino U.M.I. 7 (1990), 863–874.

T. R. Hamlett and D. Jankovic, Ideals in General Topology, General Topology and Applications, (Middletown, CT, 1988), 115 – 125; SE: Lecture Notes in Pure & Appl. Math., 123 1990, Dekker, New York.

D. Jankovic and T. R.Hamlett, New topologies from old via ideals, Amer.Math. Monthly 97 (1990), 295–310. http://dx.doi.org/10.2307/2324512

D. Jankovic and T. R.Hamlett, Compatible Extensions of Ideals, Bollettino U.M.I. 7 (1992), 453–465.

D. Jankovic, T. R. Hamlett and Ch. Konstadilaki, Local-to-global topological properties, Mathematica Japonica 52 (1) (2000), 79–81.

A. S. Mashhour, A. A. Allam, F. S. Mahmoud, F. H. Khedr, On supratopological spaces, Indian J. Pure Appl. Math. 14 (1983), 502–510.

R. L. Newcomb, Topologies which are compact modulo an ideal, Ph.D.Dissertation, Univ. of Cal. and Santa Barbara, 13 (1) 1972, 193–197.

D. V. Rancin, Compactness modulo an ideal, Soviet Math. Dokl. 13 (1) (1972), 193–197.

S. Solovjovs, Topological spaces with a countable compactness defect (in Latvian), Bachelor Thesis, Univ. of Latvia, Riga, 1999.

R. Vaidyanathaswamy, The localization theory in set-topology, Proc. Indian Acad. Sci. Math Sci. 20 (1945), 51–61.


How to Cite

I. Zvina, “On i-topological spaces: generalization of the concept of a topological space via ideals”, Appl. Gen. Topol., vol. 7, no. 1, pp. 51–66, Apr. 2006.