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Wlodek Kuperberg
Wlodek Kuperberg
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Bohr compactification as a topolicaltopological compactification

Let $G$ be a locally compact Hausdorff group. Denote its Bohr compactification withby $bG$.

Despite group structure, $G$ has several (Hausdorff) compactifications that,in in a sense, the smallest one is the one-point compactification, and the largest one is the Stone-CechČech compactification.

Is $bG$ is isomorphic to one of the (topological) compactifications of $G$ as a topological space? In the case of a positive answer, to which one? I don't know the answer even in the case of $G=\mathbb{R}$.

Bohr compactification as a topolical compactification

Let $G$ be a locally compact Hausdorff group. Denote its Bohr compactification with $bG$.

Despite group structure, $G$ has several (Hausdorff) compactifications that,in a sense, the smallest one is the one-point compactification, and the largest one is the Stone-Cech compactification.

Is $bG$ is isomorphic to one of (topological) compactifications of $G$ as a topological space? In the case of positive answer, to which one? I don't know answer even in the case of $G=\mathbb{R}$.

Bohr compactification as a topological compactification

Let $G$ be a locally compact Hausdorff group. Denote its Bohr compactification by $bG$.

Despite group structure, $G$ has several (Hausdorff) compactifications that, in a sense, the smallest one is the one-point compactification, and the largest one is the Stone-Čech compactification.

Is $bG$ is isomorphic to one of the (topological) compactifications of $G$ as a topological space? In case of a positive answer, to which one? I don't know the answer even in the case of $G=\mathbb{R}$.

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Bohr compactification as a topolical compactification

Let $G$ be a locally compact Hausdorff group. Denote its Bohr compactification with $bG$.

Despite group structure, $G$ has several (Hausdorff) compactifications that,in a sense, the smallest one is the one-point compactification, and the largest one is the Stone-Cech compactification.

Is $bG$ is isomorphic to one of (topological) compactifications of $G$ as a topological space? In the case of positive answer, to which one? I don't know answer even in the case of $G=\mathbb{R}$.