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Covering properties in countable products, II

Sachio Higuchi, Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and ${X_{n} : n \in ω}$ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y \times \prod_{n \in ω} X_{n}$ is subparacompact and (2) If ${X_{n} : n \in ω}$ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod_{n \in ω} X_{n}$ is metacompact.

Covering Properties of Continua and Mappings

Janusz J. Charatonik (2003)

Publications de l'Institut Mathématique

Cozero and Baire maps on products of uniform spaces

Gloria Tashjian (1977)

Fundamenta Mathematicae

Das Produkt von Hüllenstrukturen

Oldřich Kopeček (1971)

Archivum Mathematicum

Decomposable inverse limits with a single bonding map on [0,1] below the identity

J. Rogers (1970)

Fundamenta Mathematicae

Decomposition of topologies on lattices and hyperspaces [Book]

Costantini C., Vitolo P. (1999)

Decomposition spaces and shape in the sense of Fox

Yukihiro Kodama (1977)

Fundamenta Mathematicae

Decomposition spaces having arbitrarily small neighborhoods with 2-sphere boundaries II

Edythe Woodruff (1983)

Fundamenta Mathematicae

Decompositions into submanifolds of fixed codimension

R. J. Daverman (1986)

Banach Center Publications

Decompositions of cyclic elements of locally connected continua

D. Daniel (2010)

Colloquium Mathematicae

Let X denote a locally connected continuum such that cyclic elements have metrizable $G_{δ}$ boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.