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Introduction to topological groups. (English) Zbl 0955.54013
Summary: We present a concise survey of old and new results concerning cardinal functions on topological groups and then establish various relations between the classes of \(\sigma\)-compact, \(\aleph_0\)-bounded and \(R\)-factorizable topological groups. The article is addressed to the general topology minded reader with no (or little) experience in topological algebra.

MSC:
54H11 Topological groups (topological aspects)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
22A05 Structure of general topological groups
54D45 Local compactness, \(\sigma\)-compactness
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