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Connected Hausdorff subtopologies

Jack R. Porter — 2001

Commentationes Mathematicae Universitatis Carolinae

A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable π -weight and no connected, Hausdorff subtopology is provided.

Local cardinal functions of H-closed spaces

Angelo BellaJack R. Porter — 1996

Commentationes Mathematicae Universitatis Carolinae

The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space X is produced with the properties that | X | > 2 2 ψ ( X ) and ψ ¯ ( X ) > 2 ψ ( X ) .

On minimal- α -spaces

Giovanni Lo FaroGiorgio NordoJack R. Porter — 2003

Commentationes Mathematicae Universitatis Carolinae

An α -space is a topological space in which the topology is generated by the family of all α -sets (see [N]). In this paper, minimal- α 𝒫 -spaces (where 𝒫 denotes several separation axioms) are investigated. Some new characterizations of α -spaces are also obtained.

Maximal pseudocompact spaces

Jack R. PorterRobert M., Jr. StephensonGrant R. Woods — 1994

Commentationes Mathematicae Universitatis Carolinae

Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compactness.

H-closed functions

Filippo CammarotoVitaly V. FedorcukJack R. Porter — 1998

Commentationes Mathematicae Universitatis Carolinae

The notion of a Hausdorff function is generalized to the concept of H-closed function and the concept of an H-closed extension of a Hausdorff function is developed. Each Hausdorff function is shown to have an H-closed extension.

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