Feuilletages et topologie spectrale

Bouacida, Ezzeddine; Echi, Othman; Salhi, Ezzeddine

doi:10.2969/jmsj/05220447

Cited by 14 publications

(5 citation statements)

References 3 publications

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“…We can exhibit an infinite countable well ordered T 0 -space with only one maximal element such that every irreducible closed subset has a generic point but it cannot be the quasi-leaf space of a transversally codimension-one foliation on a closed manifold [BES,Example 3.10]. Yet for finite T 0 -spaces, we obtain Theorem 1.11.…”

Section: 22mentioning

confidence: 93%

Quasi-orbit spaces associated to T₀-spaces

Bonatti

Hattab²,

Salhi

2011

Fund. Math.

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Let G ⊂ Homeo(E) be a group of homeomorphisms of a topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. Let E/ e G be the space of classes of orbits, called the quasi-orbit space. We show that everyThe regular part X0 of a T0-space X is the union of open subsets homeomorphic to R or to S 1 . We give a characterization of the spaces X with finite singular part X − X0 which are the quasi-orbit spaces of countable groups G ⊂ Homeo+(R).Finally we show that every finite T0-space is the singular part of the quasi-leaf space of a codimension one foliation on a closed three-manifold.2010 Mathematics Subject Classification: 54F65, 54H20.

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Section: 22mentioning

confidence: 93%

Quasi-orbit spaces associated to T₀-spaces

Bonatti

Hattab²,

Salhi

2011

Fund. Math.

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“…By the way, C ⋆ -algebra and foliation theory are strongly linked. Thus, there must be some link between spectral spaces and foliation theory; this was done by the authors of [5] and [6].…”

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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“…As we have said in the introduction the concept of quasihomeomorphisms was introduced in Algebraic geometry by Grothendieck ([6], [5]). Also, it was shown that this concept arises naturally in the theory of some foliations associated to closed connected manifolds( see the papers [2] and [3]).…”

Section: Grothendieck's Quasihomeomorphisms and Yip's Quasihomeomorphmentioning

confidence: 99%

A-spectral spaces

Belaid¹,

Echi²,

Gargouri³

2004

Topology and its Applications

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This paper deals with lattice-equivalence of topological spaces. We are concerned with two questions: the first one is when two topological spaces are lattice equivalent; the second one is what additional conditions have to be imposed on lattice equivalent spaces in order that they be homeomorphic. We give a contribution to the study of these questions. Many results of Thron [Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671-679] are recovered, clarified and commented.2000 AMS Classification: 54B30, 54D10, 54F65.

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Feuilletages et topologie spectrale

Cited by 14 publications

References 3 publications

Quasi-orbit spaces associated to T₀-spaces

Quasi-orbit spaces associated to T₀-spaces

On $T_1$-reflection of topological spaces

A-spectral spaces

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Feuilletages et topologie spectrale

Cited by 14 publications

References 3 publications

Quasi-orbit spaces associated to T0-spaces

Quasi-orbit spaces associated to T0-spaces

On $T_1$-reflection of topological spaces

A-spectral spaces

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Resources

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Quasi-orbit spaces associated to T₀-spaces

Quasi-orbit spaces associated to T₀-spaces