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Samuel compactification and uniform coreflection of nearness σ -frames

Inderasan Naidoo (2006)

Czechoslovak Mathematical Journal

We introduce the structure of a nearness on a σ -frame and construct the coreflection of the category 𝐍 σ F r m of nearness σ -frames to the category 𝐊 R e g σ F r m of compact regular σ -frames. This description of the Samuel compactification of a nearness σ -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform σ -frames in [11]. We also construct the uniform coreflection of a nearness σ -frame, that is, the coreflection of the category of 𝐍 σ F r m to the category...

Sobre compactificaciones de Wallman-Frink de espacios discretos.

María Emilia Alonso García, José Javier Etayo Gordejuela, José Manuel Gamboa Mutuberria, Jesús María Ruiz Sancho (1980)

Revista Matemática Hispanoamericana

Dado un espacio T3α (X,T), es posible obtener una compactificación T2 del mismo, mediante ultrafiltros asociados a ciertas bases distinguidas de cerrados de (X,T) (Frink [4]). Se plantea así el problema siguiente: ¿Puede obtenerse toda compactificación T2 de (X,T) por este método? Desde el año 1964 en que Frink lo planteó, este interrogante ha tenido respuestas afirmativas parciales. Sin embargo, la solución definitiva es negativa.

Some remarks on the product of two C α -compact subsets

Salvador García-Ferreira, Manuel Sanchis, Stephen W. Watson (2000)

Czechoslovak Mathematical Journal

For a cardinal α , we say that a subset B of a space X is C α -compact in X if for every continuous function f X → ℝ α , f [ B ] is a compact subset of ℝ α . If B is a C -compact subset of a space X , then ρ ( B , X ) denotes the degree of C α -compactness of B in X . A space X is called α -pseudocompact if X is C α -compact into itself. For each cardinal α , we give an example of an α -pseudocompact space X such that X × X is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...

Some results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

Commentationes Mathematicae Universitatis Carolinae

A space X is truly weakly pseudocompact if X is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with χ ( x , X ) > ω for every x ∈ X ; (2) every locally bounded space is truly weakly pseudocompact; (3) for ω < κ < α , the κ -Lindelöfication of a discrete space of cardinality α is weakly pseudocompact if κ = κ ω .

Some results on sequentially compact extensions

Maria Cristina Vipera (1998)

Commentationes Mathematicae Universitatis Carolinae

The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.

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