sala posiedzeń Rady Wydziału, godz. 10:30–12:00

Taras Banakh (Lwów)
Steinhaus groups and semitopological linear spaces

Summary. By a (semi)topological linear space we understand a linear space endowed with a topology making the addition continuous and the multiplication (separately) continuous. We shall establish some properties of semitopological linear spaces, give criteria of boundedness of subsets in semitopological linear spaces, find conditions under which a semitopological linear space is a topological linear space, and present many (necessarily non-metrizable) examples of semitopological linear spaces which are not topological linear spaces. Also we shall consider the construction of a free semitopological linear space over a topological space and shall prove that for each k-space its semitopological linear space is topological. On the other hand, we shall present an example of a Tychonoff space whose free semitopological linear space differs from its free topological linear space.