Open AccessSmall and large inductive dimension for ideal topological spaces
Author(s) -
F. Sereti
Publication year - 2021
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2021.15231
Subject(s) - mathematics , dimension (graph theory) , ideal (ethics) , inductive dimension , topology (electrical circuits) , topological space , zero dimensional space , lebesgue covering dimension , dimension theory (algebra) , field (mathematics) , dimension function , complex dimension , pure mathematics , combinatorics , topological vector space , mathematical analysis , minkowski–bouligand dimension , fractal dimension , epistemology , hausdorff dimension , philosophy , fractal
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.