Displaying similar documents to “Connectedness and local connectedness of topological groups and extensions”

A generalization of amenability and inner amenability of groups

Ali Ghaffari (2012)

Czechoslovak Mathematical Journal

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Let G be a locally compact group. We continue our work [A. Ghaffari: Γ -amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of Γ -amenability of a locally compact group G defined with respect to a closed subgroup Γ of G × G . In this paper, among other things, we introduce and study a closed subspace A Γ p ( G ) of L ( Γ ) and then characterize the Γ -amenability of G using A Γ p ( G ) . Various necessary and sufficient conditions are found for a locally compact...

Linear extensions of relations between vector spaces

Árpád Száz (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let X and Y be vector spaces over the same field K . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λ F ( x ) F ( λ x ) and F ( x ) + F ( y ) F ( x + y ) for all λ K { 0 } and x , y X . After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X into Y can be extended to a linear relation F of X into Y if and only if there exists a linear subspace Z of Y such that Φ ( e ) Y | Z for all e E . Moreover, if...

A β -normal Tychonoff space which is not normal

Eva Murtinová (2002)

Commentationes Mathematicae Universitatis Carolinae

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α -normality and β -normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff β -normal non-normal space and an example of a Hausdorff α -normal non-regular space.

G δ -modification of compacta and cardinal invariants

Aleksander V. Arhangel'skii (2006)

Commentationes Mathematicae Universitatis Carolinae

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Given a space X , its G δ -subsets form a basis of a new space X ω , called the G δ -modification of X . We study how the assumption that the G δ -modification X ω is homogeneous influences properties of X . If X is first countable, then X ω is discrete and, hence, homogeneous. Thus, X ω is much more often homogeneous than X itself. We prove that if X is a compact Hausdorff space of countable tightness such that the G δ -modification of X is homogeneous, then the weight w ( X ) of X does not exceed 2 ω (Theorem 1)....