Alas, D. T. On the number of compact subsets in topological groups. (English) Zbl 0632.54001 Commentat. Math. Univ. Carol. 28, 565-568 (1987). Let \({\mathcal K}\) be the set of all compact subsets of a nondiscrete \(T_ 2\) topological group G, and \(\psi\) (G) the pseudocharacter. The boundedness number bo(G) of G is defined by the smallest infinite cardinal \(\alpha\) such that for any open neighborhood V of the unit of G, there is a subset A of G with \(| A| \leq \alpha\) so that \(V\cdot A=G\). The author proves two theorems, namely, \(\psi\) (G)\(\leq | G| \leq | {\mathcal K}| \leq bo(G)^{\psi (G)}\) and, under GCH, \(| {\mathcal K}|^{\aleph_ 0}=| {\mathcal K}|\) for a pseudocompact G. Finally there are five examples which are useful to readers. Reviewer: K.Iséki MSC: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 22A05 Structure of general topological groups Keywords:weak Lindelöf number; pseudocharacter; boundedness number PDFBibTeX XMLCite \textit{D. T. Alas}, Commentat. Math. Univ. Carol. 28, 565--568 (1987; Zbl 0632.54001) Full Text: EuDML