Convention for locally compact groups?

Question

$\bf{\text{Suppose I find the phrase:}}$

Let $G$ is a locally compact group, and $\mathcal{U}$ a basis of neighborhoods of $1$.

$\bf{\text{Question:}}$

Is it a convention to automatically take each $U\in\mathcal{U}$ to be compact?

Clearly this can be done if the need arises by the locally compact assumption on $G$, but when reading material, should this be my first interpretation such a statement?

I'd think one would specify what sort of neighborhoods are in the basis. — ncmathsadist, May 16 '13 at 01:57

score 1 · Accepted Answer · answered May 16 '13 at 01:57

1

I wouldn't think so, unless it is explicitly stated as a convention in what you are reading. (Usually, an author would explicitly signal that $U$ is a compact neighbourhood if this is what was meant.)

answered May 16 '13 at 01:57

Matt E

123,735

Convention for locally compact groups?

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