No Finite Sum Theorem for the Small Inductive Dimension of Metrizable Spaces

2019 ◽  
pp. 153-154
Author(s):  
Michael G. Charalambous
Keyword(s):  
Inductive Dimension ◽  
Sum Theorem ◽  
Small Inductive Dimension ◽  
Finite Sum ◽  
Metrizable Spaces

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>

A computing procedure for the small inductive dimension of a finite $$\mathrm{T}_0$$ T 0 -space

2014 ◽  
Vol 34 (1) ◽  
pp. 401-415 ◽  
Author(s):  
Dimitris N. Georgiou ◽  
Athanasios C. Megaritis ◽  
Seithuti P. Moshokoa
Keyword(s):  
Inductive Dimension ◽  
Small Inductive Dimension ◽  
Computing Procedure

Small and Large Inductive Dimensions of Intuitionistic Fuzzy Topological Spaces

2020 ◽  
Vol 12 (3) ◽  
pp. 413-417
Author(s):  
Abdulgawad A. Q. Al-Qubati ◽  
M-El Sayed ◽  
Hadba F. Al-Qahtani
Keyword(s):  
Topological Property ◽  
Topological Spaces ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Inductive Dimension ◽  
Small Inductive Dimension ◽  
Fuzzy Topological Spaces

The main purpose of this paper is to present some fundamental properties of small and large inductive dimensions in intuitionistic fuzzy topological spaces. Our results can be regarded as a study of their properties such as proves subset theorems, zero dimensionality and topological property of an intuitionistic fuzzy small inductive dimension. Furthermore, we introduce a large inductive dimension of intuitionistic fuzzy bi-compact and normal spaces.

Shape morphisms and components of movable compacta

1988 ◽  
Vol 103 (3) ◽  
pp. 481-486
Author(s):  
José M. R. Sanjurjo
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
The Other ◽  
Compact Metric Space ◽  
Dimension Zero ◽  
Compact Metric Spaces ◽  
Inductive Dimension ◽  
Other Hand ◽  
Small Inductive Dimension ◽  
The Relationship

The relationship between components and movability for compacta (i.e. compact metric spaces) was described by Borsuk in [5]. Borsuk proved that if each component of a compactum X is movable, then so is X. More recently Segal and Spiez[19], motivated by results of Alonso Morón[1], have constructed a (non-compact) metric space X of small inductive dimension zero and such that X is non-movable. The construction of Segal and Spiez was based on the famous space of P. Roy [16]. On the other hand, K. Borsuk gave in [5] an example of a movable compactum with non-movable components. The structure of such compacta was studied by Oledzki in [15], where he obtained an interesting result stating that if X is a movable compactum then the set of movable components of X is dense in the space of components of X. Oledzki's result was later strengthened by Nowak[14], who proved that if all movable components of a movable compactum X are of deformation dimension at most n, then so are the non-movable components and the compactum X itself.

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