A characterization of K-analyticity of groups of continuous homomorphisms

Abstract

For an abelian locally compact group X let X^p be the group of continuous homomorphisms from X into the unit circle T of the complex plane endowed with the pointwise convergence topology. It is proved that X is metrizable iff X^p is K-analytic iff X endowed with its Bohr topology σ(X,X^) has countable tightness. Using this result, we establish a large class of topological groups with countable tightness which are not sequential, so neither Fréchet-Urysohn