Small and large inductive dimension for ideal topological spaces

Authors

  • Fotini Sereti University of Patras

DOI:

https://doi.org/10.4995/agt.2021.15231

Keywords:

small inductive dimension, large inductive dimension, ideal topological space

Abstract

Undoubtedly, the small inductive dimension, ind, and the large inductive dimension, Ind, for topological spaces have been studied extensively, developing an important field in Topology. Many of their properties have been studied in details (see for example [1,4,5,9,10,18]). However, researches for dimensions in the field of ideal topological spaces are in an initial stage. The covering dimension, dim, is an exception of this fact, since it is a meaning of dimension, which has been studied for such spaces in [17]. In this paper, based on the notions of the small and large inductive dimension, new types of dimensions for ideal topological spaces are studied. They are called *-small and *-large inductive dimension, ideal small and ideal large inductive dimension. Basic properties of these dimensions are studied and relations between these dimensions are investigated.

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Author Biography

Fotini Sereti, University of Patras

Department of Mathematics

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Published

2021-10-01

How to Cite

[1]
F. Sereti, “Small and large inductive dimension for ideal topological spaces”, Appl. Gen. Topol., vol. 22, no. 2, pp. 417–434, Oct. 2021.

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