A class of maximal topologies

“…Also (X, r) is hereditarily irresolvable [7] if each of its non-empty subsets is irresolvable. (X, r) is said to be a submaximal space [1] A property P which is preserved under semi-homeomorphism [9] (ahomeomorphism [10]) is called semi-topological [9] (a-topological [11]) property, whenever semi and a-homeomorphisms are defined likewise ordinary one except continuity and openness are replaced by semi and «-corresponding ones.…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

“…In 1977, Cameron [1] gives one of the fundamental properties of spaces which called submaximality. Also, several weaker types than openness of sets have been defined throughout the last twenty years ago, by a great staff of topologiests.…”

Section: Introductionmentioning

confidence: 99%

A Note on Submaximal Spaces and SMPC Functions

Mahmoud¹,

Rose²

1995

Demonstratio Mathematica

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“…Maximal feebly compact spaces were studied in [4,12,13]. In [3] the maximality of this class was studied in the realm of Tychonoff spaces.…”

Section: Introductionmentioning

confidence: 99%

Maximal pseudocompact spaces and the Preiss-Simon property

2013

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We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y . It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under continuous images while this is not true for the class of countably compact spaces. We prove that every Fréchet-Urysohn compact space is homeomorphic to a retract of a compact MP-space. We also give a ZFC example of a Fréchet-Urysohn compact space which is not maximal pseudocompact. Therefore maximal pseudocompactness is not preserved by continuous images in the class of compact spaces. MSC: 54D99, 54B10Keywords

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A class of maximal topologies

Cited by 21 publications

References 8 publications

Singular sets and maximal topologies

Singular sets and maximal topologies

A Note on Submaximal Spaces and SMPC Functions

Maximal pseudocompact spaces and the Preiss-Simon property

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