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

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?

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    $\begingroup$ I'd think one would specify what sort of neighborhoods are in the basis. $\endgroup$ – ncmathsadist May 16 '13 at 1:57
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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.)

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