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Compact Pseudo-Convergences.

C.H. Cook (1973)

Mathematische Annalen

Compact scattered spaces in forcing extensions

Kenneth Kunen (2005)

Fundamenta Mathematicae

We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models of $2^{ℵ ₀} = ℵ ₂$ in which no such space can have ℵ₂ countable levels.

Compact sets without converging sequences in the random real model.

Dow, A., Fremlin, D. (2007)

Acta Mathematica Universitatis Comenianae. New Series

Compact spaces homeomorphic to a ray of ordinals

John Baker (1972)

Fundamenta Mathematicae

Compact spaces that do not map onto finite products

Antonio Avilés (2009)

Fundamenta Mathematicae

We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.

Compact topologically torsion elements of topological abelian groups

Peter Loth (2005)

Rendiconti del Seminario Matematico della Università di Padova

Compact unions of closed subsets are closed and compact intersections of open subsets are open

Nachbin, Leopoldo (1992)

Portugaliae mathematica

Compact widths in metric trees

Asuman Güven Aksoy, Kyle Edward Kinneberg (2011)

Banach Center Publications

The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also...

Compacta are maximally $G_{δ}$ -resolvable

István Juhász, Zoltán Szentmiklóssy (2013)

Commentationes Mathematicae Universitatis Carolinae

It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $Δ (X)$ many pairwise disjoint dense subsets, where $Δ (X)$ denotes the minimum size of a non-empty open set in $X$ . The aim of this note is to prove the following analogous result: Every compactum $X$ contains $Δ_{δ} (X)$ many pairwise disjoint $G_{δ}$ -dense subsets, where $Δ_{δ} (X)$ denotes the minimum size of a non-empty $G_{δ}$ set in $X$ .