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Closed embeddings into complements of Σ -products

Aleksander V. Arhangel'skii, Miroslav Hušek (2008)

Commentationes Mathematicae Universitatis Carolinae

In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a Σ -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and...

Closed subsets of absolutely star-Lindelöf spaces II

Yan-Kui Song (2003)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed G δ subspace.

Coarse dimensions and partitions of unity.

N. Brodskiy, J. Dydak (2008)

RACSAM

Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.

Coarse structures and group actions

N. Brodskiy, J. Dydak, A. Mitra (2008)

Colloquium Mathematicae

The main results of the paper are: Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X. Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied: (1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂. (2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...

Compactifications and uniformities on sigma frames

Joanne L. Walters-Wayland (1991)

Commentationes Mathematicae Universitatis Carolinae

A bijective correspondence between strong inclusions and compactifications in the setting of σ -frames is presented. The category of uniform σ -frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the σ -frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.

Currently displaying 61 – 80 of 388