Character and pseudocharacter in minimal topological groups (Q1076818)

For any uncountable cardinal \(\tau\) the author constructs a (totally) minimal topological group G with \(\psi (G)=\aleph_ 0\) and \(\chi (G)=\tau\). Thus he answers in the negativ the well-known question rised by A. V. Arkhangel'skij whether the pseudocharacter and the character of each minimal topological group coincide. Morover, an elegant author's construction shows that for any free group H with \(| H| =\tau \geq \aleph_ 0\) there exists a totally minimal topological group topology \({\mathcal T}\) on H such that \(\psi\) (H,\({\mathcal T})=\aleph_ 0\) and \(\chi\) (H,\({\mathcal T})=\tau\). The problem of Arkhangel'skij was also solved independently by I. I. Guran and V. G. Pestov.