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

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


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?

  • 2
    $\begingroup$ I'd think one would specify what sort of neighborhoods are in the basis. $\endgroup$ – ncmathsadist May 16 '13 at 1:57

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.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.