Asking for more trouble

Asking for more trouble

[Michael Barr]

G is now talking about locally compact spaces and there are two phrases I
have not seen.  One is "relatively compact".  I assume this is the same as
what I call "conditionally compact", i.e. having compact closure.  The
other is "denombrable".  The context is "Suppose that the locally compact
space $X$ is denombrable a l'infini".  Does it mean first countable?

I don't want to start a discussion what bad terms these are, I just want
to know what they mean.

Michael

Re: Asking for more trouble

[Toby Bartels]

Michael Barr wrote in part:

>G is now talking about locally compact spaces and there are two phrases I
>have not seen.  One is "relatively compact".  I assume this is the same as
>what I call "conditionally compact", i.e. having compact closure.

Depending on the author, "relatively compact" can mean either
having compact closure, or having *any* compact superset.
In a Hausdorff space, these are equivalent.


--Toby

Re: Asking for more trouble

[Johannes.Huebschmann]

These are Bourbaki terms.

Denombrable: countable

denombrable a l'infini: countable at infinity
(the point at infinity of the Alexandroff compactification
of a locally compact space has a countable neighborhood base)

relativement compact: relatively compact (having compact closure)


Johannes



> G is now talking about locally compact spaces and there are two phrases I
> have not seen.  One is "relatively compact".  I assume this is the same as
> what I call "conditionally compact", i.e. having compact closure.  The
> other is "denombrable".  The context is "Suppose that the locally compact
> space $X$ is denombrable a l'infini".  Does it mean first countable?
>
> I don't want to start a discussion what bad terms these are, I just want
> to know what they mean.
>
> Michael
>
>
>