Research and Exposition in Mathematics -- Volume 31
Enlarged Picture
Gábor Lukács
Compact-like Topological Groups
xiv+166 pages, soft cover, ISBN 978-3-88538-231-7, EUR 28.00, 2009
The class of compact topological groups is perhaps the most understood
part of topological groups. This monograph deals with larger classes
defined by properties shared by compact groups. For instance, if G is
a compact topological group, then for every group H, the image of every
closed subgroup of G × H under the second projection is closed in
H. Topological groups with this property are called c-compact.
Is every c-compact topological group compact?
Chapter 1 is an elementary introduction to topological groups.
Chapter 2 presents cardinal invariants, a more specialized aspect of
topological group theory.
Chapter 3 focuses on two compactness-like properties, namely,
precompactness and minimality.
Chapter 4 relates to the main question by proving compactness
theorems (that is, results of the type: if G is c-compact and
has an additional property, then G is compact), open mapping
theorems, and reduction theorems (reducing the general
question to smaller classes of groups).
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