Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
the entry neighbourhood base was in a funny state. I have edited a little. No mention of filters yet.
I edited a little myself.
That makes sense, thanks.
I edited some more: I removed the superscripts $x$ as superfluous (and overly busy as notation), and removed the word “open” preceding the $U_i$ since there is no insistence on that (as when one says, “a base of compact neighborhoods”, etc.).
Sure. I had added those superscripts to amplify that the base elements are all required to be neighbourhoods of $x$, too, instead of more general open subsets. I sometimes see that condition being omitted (forgotten).
Not requiring the neighbourhoods to be open, in my mind, helps to remember that they're supposed to be neighbourhoods of something. (Because otherwise there's no restriction at all!) There's open sets, and then there's neighbourhoods.
1 to 6 of 6