Topological Groups: Yesterday, Today, Tomorrow

• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2016
• Subjects: Hilbert's 5th problem; structure theory; duality and reflexivity; paratopological groups; (locally) minimal topological groups; characterized subgroups; locally compact groups; representations; compact groups; suitable sets for topological groups; covering theory for topological groups; topological groups; transformation groups; Lie groups; pro-Lie groups; compactness conditions in topological groups; profinite groups; free topological groups; almost periodic
• Online Access: DOAB: download the publication; DOAB: description of the publication

In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century. It required half a century of effort by several generations of em...