A-spectral spaces

Belaid, Karim; Echi, Othman; Gargouri, Riyadh

doi:10.1016/j.topol.2003.08.009

Cited by 10 publications

(4 citation statements)

References 6 publications

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“…Recall that a topological space is said to be spectral if it is homeomorphic to the spectrum of a ring equipped with the Zariski topology. In [4] Remark 2.5. The Khalimsky line and Khalimsky plane are T 0 (that is, whenever x and y are distinct points of X, there exists an open set which contains one of them but not the other) and are not T 1 (that is, {x} = {x}, for each x ∈ X).…”

Section: A Subset S Of X Is Said To Be Irreducible If Every Two Non mentioning

confidence: 99%

“…More precisely, the fact that, the topological gradient approach do not give necessary closed contours make the results of the segmentation process not suitable enough. On the other part, from 2004 to 2013 K. Belaid et al [4,5,6,1] have studied some topological spaces and compactifications. More precisely, let Y be a topological space and let X be a subset of Y. Y is said to be a compactification of X, if the following properties are verified:…”

Section: Introductionmentioning

confidence: 99%

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On Khalimsky topology and applications on the digital image segmentation

Hajri¹,

Belaid²,

Belaid³

2015

ams

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The main goal of this work is to deal with the Khalimsky digital topology and its application in segmentation. First, we begin by giving some theoretical results on Khalimsky topology, the one point compactification and separation axioms. Then, we present and discuss digital applications in imaging. More precisely, numerical results on segmentation, contours detection and skeletonization are proposed. We end this paper by some concluding remarks.

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Section: A Subset S Of X Is Said To Be Irreducible If Every Two Non mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Khalimsky topology and applications on the digital image segmentation

Hajri¹,

Belaid²,

Belaid³

2015

ams

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“…Recently, some authors (for example [2] and [3]) have been interested on particular type of spectral spaces constructed from some compactifications (namely, the one pointcompactification for [3], and the Walman compactification and the T 0 -compactification for [2]).…”

Section: T 1 -Spectral Spacesmentioning

confidence: 99%

On $T_1$-reflection of topological spaces

Lazaar

Mhemdi

Al-shami

et al. 2023

Hacettepe Journal of Mathematics and Statistics

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This paper deals with some universal spaces. For every topological space $X$, the universal $T_1$ space is viewed as the bottom element of the lattice $\mathcal{L}_X$. The class of morphisms in $\mathrm{\mathbf{Top}}$ orthogonal to all $T_1$ spaces is characterized. Also, we introduce some new separation axioms and characterize them. Moreover, we characterize topological spaces $X$ for which the universal $T_1$ space associated with $X$ is a spectral space. Finally, we give some characterizations of topological spaces such that their $T_1$-reflection are compact spaces.

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“…Compact scattered spaces have found important use in analysis and topology (see for example [10] in which S. M r o w k a, M. R a j a g o p a l a n, T. S o u n d ar a r a j a n characterized compact scattered Hausdorff spaces). On the other hand, from 2004 to 2015 K. B e l a i d et al [1], [4], [5] studied some topological spaces and compactifications. Section 2 is devoted to a short study of digital spaces and to a characterization of the subspace A to get its closure scattered.…”

Section: Introductionmentioning

confidence: 99%