Scattered Spaces, Compactifications and an Application to Image Classification Problem

Al-Hajri, Monerah; Belaid, Karim; Belaid, Lamia Jaafar

doi:10.1515/tmmp-2016-0015

Cited by 2 publications

(2 citation statements)

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“…In the field of image analysis, classification of images of a compact universe become easier. In [13] Hajri et al, studied the compactification of a scattered space. A topological space U is said to be scattered if every non-empty subset X of U contains at least one isolated point.…”

Section: Topological Structures On Rough Sets Generated By Equivalence Relationsmentioning

confidence: 99%

Topological structures in rough set theory: A survey

Singh

Tiwari

2020

Hacettepe Journal of Mathematics and Statistics

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Rough set theory provides a mathematical tool to study vague, imprecise, inconsistent and uncertain knowledge. The topological notions are closely related to the notions and results of rough set theory, so the conjoint study of rough set theory and topology becomes essential. Researchers have widely discussed the topological aspects and their applications in rough set theory. This study highlights the inter dependencies of topology and classical rough set theory and the significant work done in this area during the last twenty years. Mathematics Subject Classification (2010).

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Section: Topological Structures On Rough Sets Generated By Equivalence Relationsmentioning

confidence: 99%

Topological structures in rough set theory: A survey

Singh

Tiwari

2020

Hacettepe Journal of Mathematics and Statistics

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“…In 2016, Al-Hajri and others characterized spaces such that their Aleksandrov (one-poin) compactification is a scattered space. They presented image classificaiton problem as an application of scattered space [2]. In 2018, Cioban and Budanaev present some geometrical and topological concepts to accommodate the needs of information theories.…”

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confidence: 99%

Fan-Gottesman Compactification and Scattered Spaces

Elmali

Ugur

2020

Applied Mathematics and Nonlinear Sciences

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Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space X is said to be scattered if every nonempty subset S of X contains at least one point which is isolated in S. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan-Gottesman compactification of T3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification X* is a scattered.

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Scattered Spaces, Compactifications and an Application to Image Classification Problem

Cited by 2 publications

References 10 publications

Topological structures in rough set theory: A survey

Topological structures in rough set theory: A survey

Fan-Gottesman Compactification and Scattered Spaces

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