Let H be a countable subgroup of the metrizable compact abelian group G and f : H → T = R/Z a (not necessarily continuous) character of H . Then there exists a sequence (χn) ∞ n=1 of (continuous) characters of G such that limn→∞ χn(α) = f(α) for all α ∈ H and (χn(α)) ∞ n=1 does not converge whenever α ∈ G \ H . If one drops the countability and metrizability requirement one can obtain similar r...

In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a <r-point-finite base and a LOTS with a point-countable base is paracompact. An example of a LOTS with a point-countable base that does not have a <r-point-finite base is given. Conditions are given for the metrizabilit...

The starting point of the famous structure theorems on Berwald spaces due to Z.I. Szabó [4] is an observation on the Riemann-metrizability of positive definite Berwald manifolds. It states that there always exists a Riemannian metric on the underlying manifold such that its Levi-Civita connection is just the canonical connection of the Berwald manifold. In this paper we present a new elementary...