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Let $Ψ (Σ)$ be the Isbell-Mr’owka space associated to the $M A D$ -family $Σ$ . We show that if $G$ is a countable subgroup of the group $𝐒 (ω)$ of all permutations of $ω$ , then there is a $M A D$ -family $Σ$ such that every $f \in G$ can be extended to an autohomeomorphism of $Ψ (Σ)$ . For a $M A D$ -family $Σ$ , we set $I n v (Σ) = {f \in 𝐒 (ω) : f [A] \in Σ$ for all $A \in Σ}$ . It is shown that for every $f \in 𝐒 (ω)$ there is a $M A D$ -family $Σ$ such that $f \in I n v (Σ)$ . As a consequence of this result we have that there is a $M A D$ -family $Σ$ such that $n + A \in Σ$ whenever $A \in Σ$ and $n < ω$ , where $n + A = {n + a : a \in A}$ for $n < ω$ . We also notice that there is no $M A D$ -family $Σ$ such...

Convergence functions and their related topologies

D. Kent (1964)

Fundamenta Mathematicae

Convergence in exponentiable spaces.

Pisani, Claudio (1999)

Theory and Applications of Categories [electronic only]

Convergence in Relational Structures.

W. TAYLOR (1970)

Mathematische Annalen

Convergence of convex-concave saddle functions : applications to convex programming and mechanics

Dominique Azé, Hedy Attouch, Roger J.-B. Wets (1988)

Annales de l'I.H.P. Analyse non linéaire

Convergence of sequences of real functions with respect to small systems

Jerzy Niewiarowski (1988)

Mathematica Slovaca

Convergence structures

Hearsey, B.V., Kent, D.C. (1972)

Portugaliae mathematica

Convergence Structures on Homeomorphism Groups.

Wayne R. Park (1972)

Mathematische Annalen

Convergence with respect to $F_{σ}$ -supported ideals

Jacek Hejduk (1997)

Colloquium Mathematicae

Convergences et relations compactantes. Application aux équilibres de Stackelberg

Jean Guillerme (1993)

Rendiconti del Seminario Matematico della Università di Padova

Convergences $𝔏_{S}^{H}$ for the group of real numbers

Josef Novák (1993)

Czechoslovak Mathematical Journal

Convergencia En Relacion.

Nicolás M. Zalote (1988)

Revista colombiana de matematicas

Convergent Filter Bases

Roland Coghetto (2015)

Formalized Mathematics

We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).

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