Rationals with exotic convergences
Roman Frič · Czech digital mathematics library · 1989
RATIONALS WITH EXOTIC CONVERGENCES ROMAN FRICWe study properties of rational numbers equipped with various sequential and filter convergence structures coarser than the usual metric convergence.In particular, we show that rational numbers can be equipped with both sequential and filter convergence structures compatible with a given algebraic structure (group, ring, vector structure over Q) such that no two rational numbers can be separated by disjoint neighbourhoods.Consequently, all continuous mappings of the resulting space are constant.After proving the "sequential" results directly, the corresponding "filter" results will follow immediately by applying the coarse first countable filter modification functor, recently introduced by R. Beattie and H.-P. Butzmann.