On resolvable primal spaces

Dahane, Intissar; Lazaar, Sami; Richmond, Tom; Turki, Tarek

doi:10.2989/16073606.2018.1437093

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Cited by 9 publications

(1 citation statement)

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“…The notion of principal space introduced by [1], with the name of Diskrete Raume, is a topological space in which any intersections of open sets is also open. Later on, this kind of topologies has been called as principal spaces [5,18,19,20,22,25].…”

Section: Introductionmentioning

confidence: 99%

Generating methods for principal topologies on bounded lattices

Karaçal¹,

Ertuğrul²,

Kesicioğlu³

2021

Kybernetika

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Section: Introductionmentioning

confidence: 99%

Generating methods for principal topologies on bounded lattices

Karaçal¹,

Ertuğrul²,

Kesicioğlu³

2021

Kybernetika

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The Lattice of Functional Alexandroff Topologies

Menix

Richmond

2020

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Quasiorders for a Characterization of Iso-dense Spaces

Richmond,

Wajch

2024

Bull. Malays. Math. Sci. Soc.

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A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in $$\textbf{ZF}$$ ZF a new characterization of iso-dense spaces in terms of special quasiorders. For a non-empty family $$\mathcal {A}$$ A of subsets of a set X, a quasiorder $${{\,\mathrm{\lesssim }\,}}_{\mathcal {A}}$$ ≲ A on X determined by $$\mathcal {A}$$ A is defined. Necessary and sufficient conditions for $$\mathcal {A}$$ A are given to have the property that the topology consisting of all $${{\,\mathrm{\lesssim }\,}}_{\mathcal {A}}$$ ≲ A -increasing sets coincides with the generalized topology on X consisting of the empty set and all supersets of non-empty members of $$\mathcal {A}$$ A . The results obtained, applied to the quasiorder $${{\,\mathrm{\lesssim }\,}}_{\mathcal {D}}$$ ≲ D determined by the family $$\mathcal {D}$$ D of all dense sets of a given (generalized) topological space, lead to a new characterization of non-trivial iso-dense spaces. Independence results concerning resolvable spaces are also obtained.

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On resolvable primal spaces

Cited by 9 publications

References 16 publications

Generating methods for principal topologies on bounded lattices

Generating methods for principal topologies on bounded lattices

The Lattice of Functional Alexandroff Topologies

Quasiorders for a Characterization of Iso-dense Spaces

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