Completeness of sequential convergence groups
Let be the Isbell-Mr’owka space associated to the -family . We show that if is a countable subgroup of the group of all permutations of , then there is a -family such that every can be extended to an autohomeomorphism of . For a -family , we set for all . It is shown that for every there is a -family such that . As a consequence of this result we have that there is a -family such that whenever and , where for . We also notice that there is no -family such...
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).