Unions of chains in dyadic compact spaces and topological groups

The following problem is considered: If a topological group G is the union of an increasing chain of subspaces and certain cardinal invariants of the subspaces are known, what can be said about G? We prove that if G is locally compact and every subspace in the chain has countable pseudocharacter or tightness, then G is metrizable. We also prove a similar assertion for σ-compact and totally bounded groups represented as the union of first countable subspaces, when the length of the chain is a regular cardinal greater than ω1. Finally, we show that these results are not valid in general, not even for compact spaces.