Fat Delta 2: functorial subgroups of topological abelian groups
Keywords:
functorial subgroup, (locally) compact abelian group, (locally) precompact group, maximally almost periodic group, minimally almost periodic group, Pontryagin Duality, torus, quasi-torsion element, reflexive, topologically $p$ torsion element, dually embedded subgroup, von Neumann kernelAbstract
In the predecessor [16] of this paper the canonical subgroup (Fat Delta) $\boldsymbol{\Delta}(G)$ of a compact abelian group $G$ was studied. It is the sum of all closed disconnected subgroups of $G$ and it appeared before in the literature (see [28]) as $\operatorname{td}(G)$, defined for arbitrary topological groups and motivated by completely different considerations. We introduce and compare further functorial subgroups of general topological groups and study their relationships with $\boldsymbol{\Delta}(G)$ and $\operatorname{td}(G)$.
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