Ordered separation axioms and the Wallman ordered compactification

Künzi, Hans-Peter A.; McCluskey, Aisling; Richmond, Tom

doi:10.5486/pmd.2008.4251

Publ. Math. Debrecen

2008

DOI: 10.5486/pmd.2008.4251

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Ordered separation axioms and the Wallman ordered compactification

Hans-Peter A. Künzi¹,

Aisling McCluskey²,

Tom Richmond³

Abstract: Two constructions have been given previously of the Wallman ordered compactification w0X of a T1-ordered, convex ordered topological space (X, τ, ≤). Both of those papers note that w0X is T1, but need not be T1-ordered. Using this as one motivation, we propose a new version of T1-ordered, called T K 1 -ordered, which has the property that the Wallman ordered compactification of a T K 1 -ordered topological space is T K 1 -ordered. We also discuss the R0-ordered (R K 0 -ordered) property, defined so that an ord… Show more

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Cited by 3 publications

References 11 publications

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Lower separation axioms in bitopogenous spaces

Richmond,

Šlapal

2024

Mathematica Slovaca

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Several naturally defined lower separation axioms for bitopological spaces obtained by modifying the axioms T 0, T 1, and R 0 appear in the literature. We introduce and study analogous separation axioms for bitopogenous spaces. In particular, we investigate relationships between the axioms and discuss the conditions under which the relationships are similar to those between the corresponding separation axioms for bitopological spaces.

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Lower separation axioms in bitopogenous spaces

Richmond,

Šlapal

2024

Mathematica Slovaca

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F-door spaces and F-submaximal spaces

Dridi¹,

Lazaar

Turki

2013

Appl.Gen.Topol.

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Submaximal spaces and door spaces play an enigmatic role in topology.In this paper, reinforcing this role, we are concerned with reaching two main goals: The first one is to characterize topological spaces X such that F(X) is a submaximal space (resp., door space) for some covariant functor F from the category Top to itself. T0, ρ and FH functors are completely studied. Secondly, our interest is directed towards the characterization of maps f given by a flow (X, f ) in the category Set, such that (X, P(f )) is submaximal (resp., door) where P(f ) is a topology on X whose closed sets are exactly the f -invariant sets.

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On some properties of $T_0$-ordered reflection

Lazaar

Mhemdi

2014

Appl.Gen.Topol.

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In [12], the authors give an explicit construction of the T0−ordered reflection of an ordered topological space (X, τ, ≤). All ordered topological spaces such that whose T0−ordered reflections are T1−ordered spaces are characterized. In this paper, some properties of the T0−ordered reflection of a given ordered topological space (X, τ, ≤) are studies. The class of morphisms in ORDTOP orthogonal to all T0−ordered topological space is characterized.

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Ordered separation axioms and the Wallman ordered compactification

Cited by 3 publications

References 11 publications

Lower separation axioms in bitopogenous spaces

Lower separation axioms in bitopogenous spaces

F-door spaces and F-submaximal spaces

On some properties of $T_0$-ordered reflection

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