Annales Mathematicae Silesianae, Nr 13 (1985), s. 155-162
The firs t p a r t of the pape r is devoted to topological analogies
of some theorems from re a l analysis (Vitali’s covering theorem, Lebesgue theorem
o n oute r density, Smital’s lemma). Then we give a topological analogue of a theorem
of Ostrowski connected with additive functions.
In the la st p a r t we deal w ith Hamel bases, specially w ith Burstin bases. We
prove th e ir existence and study topological and measure properties.