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15
47
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Showing that the identity (path) component of a matrix group is a matrix group

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#lie-groups #topological-groups #linear-groups
42
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Show that $(C^{k}([0,1],F),\left \| . \right \|_{C^{k}})$ is banach , where $(F,\left \| . \right \|_{F})$ is banach

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#real-analysis #vector-spaces #banach-spaces #cauchy-sequences #topological-groups
66
Views

Projective Limits of Compact Groups: Exact or Not?

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#general-topology #homological-algebra #topological-groups #separation-axioms #limits-colimits
107
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Is $\mathbb{Z}$ discrete in $\widehat{\mathbb{Z}}$?

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#abstract-algebra #general-topology #galois-theory #algebraic-number-theory #topological-groups
49
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Proving that $H_e$ is a subgroup of $G$

Published on
#group-theory #normal-subgroups #topological-groups
95
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Is a Polish subgroup of a Lie group Lie?

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#group-theory #lie-groups #topological-groups
62
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$GL(n, \mathbb{C})$ is not residually finite

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#general-topology #group-theory #solution-verification #topological-groups #general-linear-group
61
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Action of a crystallographic group on $\mathbb{R}^n$

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#group-actions #topological-groups #isometry #crystallography #proper-maps
56
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Are products of 2 continuous maps on topological space still continuous?

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#group-theory #algebraic-topology #topological-groups
168
Views

If a monothetic group is locally compact, then it is either discrete or compact

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#general-topology #compactness #topological-groups #locally-compact-groups
106
Views

If a discrete group acts on a compact metric space with an infinite invariant set, is it cyclic?

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#general-topology #metric-spaces #compactness #cyclic-groups #topological-groups
32
Views

Why the addition group of a local field is isomorphic to its character group?

Published on
#number-theory #topological-groups #local-field #locally-compact-groups
123
Views

Lie algebra-Lie group correspondence of an exact sequence

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#lie-groups #lie-algebras #topological-groups #exact-sequence
86
Views

Extending the definition of convolution product on $\mathcal{F}(C(G))$, $G$ abelian compact group

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#fourier-analysis #fourier-transform #convolution #harmonic-analysis #topological-groups
111
Views

Differential of a smooth map computation

Published on
#differential-topology #topological-groups

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