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$E$ -sequential envelopes

Roman Frič, Miroslav Hušek (1979)

Commentationes Mathematicae Universitatis Carolinae

Each concrete category has a representation by $T_{2}$ paracompact topological spaces

Václav Koubek (1974)

Commentationes Mathematicae Universitatis Carolinae

Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Andrei Sivak (1996)

Fundamenta Mathematicae

We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in $ℝ^{n}$ , n ≥ 1, is a σ-limit set for some continuous map.

Eberlein spaces of finite metrizability number

István Juhász, Zoltán Szentmiklóssy, Andrzej Szymański (2007)

Commentationes Mathematicae Universitatis Carolinae

Yakovlev [On bicompacta in $Σ$ -products and related spaces, Comment. Math. Univ. Carolin. 21.2 (1980), 263–283] showed that any Eberlein compactum is hereditarily $σ$ -metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.

Économie et théorie des catastrophes

Yves Balasko (1978)

Mathématiques et Sciences Humaines

Les hypothèses de différentiabilité jouent un rôle essentiel dans plusieurs travaux récents consacrés à l'étude des propriétés de l'équilibre économique. Cet article présente une synthèse aussi élémentaire que possible d'une partie de ces travaux et fait aussi le lien avec la théorie des catastrophes de Thom.

Editorial

Irina Perfilieva, Michael Wagenknecht (2009)

Acta Mathematica Universitatis Ostraviensis

Egoroff, σ, and convergence properties in some archimedean vector lattices

A. W. Hager, J. van Mill (2015)

Studia Mathematica

An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each ${a ₙ}_{n \in ℕ} c o n A ⁺$ there are ${λ ₙ}_{n \in ℕ} \subseteq (0, \infty)$ and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent, and equivalent...