Covering dimension and ideal topological spaces

2020 ◽  
pp. 1-16
Author(s):  
A.C. Megaritis
Keyword(s):  
Topological Spaces ◽  
Covering Dimension

Four-Dimension Equivalences

1968 ◽  
Vol 20 ◽  
pp. 48-50 ◽  
Author(s):  
J. R. Gard ◽  
R. D. Johnson
Keyword(s):  
Topological Spaces ◽  
Covering Dimension ◽  
Closed Set ◽  
Set Separation

The object of this paper is to establish the equivalence of four functionrelated dimension concepts in arbitrary topological spaces. These concepts involve stability of functions (3, p. 74), the modification of covering dimension involving basic covers (1, p. 243) (which is equivalent to Yu. M. Smirnov's definition using normal covers), the definition involving essential mappings (2, p. 496), and a modification of the closed set separation characterization of dimension in (3, p. 35).

scholarly journals Small and large inductive dimension for ideal topological spaces

2021 ◽  
Vol 22 (2) ◽  
pp. 417
Author(s):  
Fotini Sereti
Keyword(s):  
Topological Spaces ◽  
Covering Dimension ◽  
Basic Properties ◽  
Inductive Dimension ◽  
Initial Stage ◽  
Small Inductive Dimension ◽  
Important Field

<p>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.</p>

scholarly journals Covering dimension and normality in L-topological spaces

2012 ◽  
Vol 6 (1) ◽  
pp. 35
Author(s):  
Thankachan Baiju ◽  
Jacob John Sunil
Keyword(s):  
Topological Spaces ◽  
Covering Dimension

scholarly journals A study of the quasi covering dimension of Alexandroff countable spaces using matrices

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6327-6337
Author(s):  
D.N. Georgiou ◽  
A.C. Megaritis ◽  
F. Sereti
Keyword(s):  
Matrix Algebra ◽  
Computational Procedure ◽  
Topological Spaces ◽  
Topological Dimension ◽  
Covering Dimension ◽  
Alexandroff Space ◽  
Countable Space ◽  
Different Types ◽  
The Matrix

The notion of Alexandroff space was firstly appeared in [1]. Different types of the covering dimension in the set of all Alexandroff countable spaces have been studied (see [5]). Inspired by [9], where a new topological dimension, called quasi covering dimension was developed, in this paper we study this new dimension in the set of all Alexandroff countable topological spaces using the matrix algebra. Especially, we characterize the open and dense subsets of an arbitrary Alexandroff countable space X using matrices. Under certain additional requirements on X, we provide a computational procedure for the determination of the quasi covering dimension of X.

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