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Continuous functions between Isbell-Mrówka spaces

Salvador García-Ferreira (1998)

Commentationes Mathematicae Universitatis Carolinae

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 G can be extended to an autohomeomorphism of Ψ ( Σ ) . For a M A D -family Σ , we set I n v ( Σ ) = { f 𝐒 ( ω ) : f [ A ] Σ for all A Σ } . It is shown that for every f 𝐒 ( ω ) there is a M A D -family Σ such that f 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 Σ whenever A Σ and n < ω , where n + A = { n + a : a A } for n < ω . We also notice that there is no M A D -family Σ such...

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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