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We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

$π$ -mappings in $l s$ -Ponomarev-systems

Nguyen Van Dung (2011)

Archivum Mathematicum

We use the $l s$ -Ponomarev-system $(f, M, X, {𝒫_{λ, n}})$ , where $M$ is a locally separable metric space, to give a consistent method to construct a $π$ -mapping (compact mapping) with covering-properties from a locally separable metric space $M$ onto a space $X$ . As applications of these results, we systematically get characterizations of certain $π$ -images (compact images) of locally separable metric spaces.

$σ$ -discrete decomposability of completely additive families

Frolík, Zdeněk, Holický, Petr (1976)

Seminar Uniform Spaces

$σ$ -porosity in monotonic analysis with applications to optimization.

Rubinov, A.M. (2005)

Abstract and Applied Analysis

$σ$ -porosity is separably determined

Marek Cúth, Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

We prove a separable reduction theorem for $σ$ -porosity of Suslin sets. In particular, if $A$ is a Suslin subset in a Banach space $X$ , then each separable subspace of $X$ can be enlarged to a separable subspace $V$ such that $A$ is $σ$ -porous in $X$ if and only if $A \cap V$ is $σ$ -porous in $V$ . Such a result is proved for several types of $σ$ -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...

$Σ$ -products and selections of set-valued mappings

Ivailo Shishkov (2001)

Commentationes Mathematicae Universitatis Carolinae

Every lower semi-continuous closed-and-convex valued mapping $Φ : X \to 2^{Y}$ , where $X$ is a $Σ$ -product of metrizable spaces and $Y$ is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

$Σ$ -products of paracompact Čech-scattered spaces

Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we shall discuss $Σ$ -products of paracompact Čech-scattered spaces and show the following: (1) Let $Σ$ be a $Σ$ -product of paracompact Čech-scattered spaces. If $Σ$ has countable tightness, then it is collectionwise normal. (2) If $Σ$ is a $Σ$ -product of first countable, paracompact (subparacompact) Čech-scattered spaces, then it is shrinking (subshrinking).

$Σ_{s}$ -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

We show that any $Σ_{s}$ -product of at most $𝔠$ -many $L Σ (\leq ω)$ -spaces has the $L Σ (\leq ω)$ -property. This result generalizes some known results about $L Σ (\leq ω)$ -spaces. On the other hand, we prove that every $Σ_{s}$ -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every $Σ_{s}$ -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

σ-ideals and related Baire systems

R. Mauldin (1971)

Fundamenta Mathematicae

Σ-spaces

Keiô Nagami (1969)

Fundamenta Mathematicae

$τ$ -distance in a general topological space $(X, τ)$ with application to fixed point theory.

Aamri, M., el Moutawakil, D. (2003)

Southwest Journal of Pure and Applied Mathematics [electronic only]

$τ$ -pseudocompact mappings.

Mironova, Yu.N. (2001)

Sibirskij Matematicheskij Zhurnal

$ϕ ψ$ -continuity between two pointwise quasi-uniformity spaces.

Daraby, Bayaz (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

$ω$ H-sets and cardinal invariants

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

A subset $A$ of a Hausdorff space $X$ is called an $ω$ H-set in $X$ if for every open family $𝒰$ in $X$ such that $A \subset ⋃ 𝒰$ there exists a countable subfamily $𝒱$ of $𝒰$ such that $A \subset ⋃ {\bar{V} : V \in 𝒱}$ . In this paper we introduce a new cardinal function $t_{s θ}$ and show that $| A | \leq 2^{t_{s θ} (X) ψ_{c} (X)}$ for every $ω$ H-set $A$ of a Hausdorff space $X$ .

$ω_{μ}$ -additive topological spaces

Giuliano Artico, Roberto Moresco (1982)

Rendiconti del Seminario Matematico della Università di Padova

$ω_{μ}$ -metric spaces and $ω_{μ}$ -proximities

Fredrick Stevenson (1971)

Fundamenta Mathematicae

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