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Concept
Locally Compact Group
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Summary
A
Locally Compact Group
is a
Topological Group
that has a
Local Base
of
Compact neighborhoods
around the
Identity Element
, providing a natural setting for
Harmonic Analysis
and
Representation Theory
. These groups generalize the notion of
Compact groups
and are crucial in the study of
Lie Groups
and
Algebraic Groups
, bridging the gap between discrete and
Continuous Symmetries
.
Concepts
Topological Group
Compact Space
Haar Measure
Lie Group
Algebraic Group
Harmonic Analysis
Representation Theory
Locally Compact Space
Borel Set
Pontryagin Duality
Topological Groups
Mackey's Theorem
Relevant Degrees
Algebra 100%
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