Date: Jan 2, 2013 3:43 AM
Author: William Elliot
Subject: Re: Cech Stone Compactification

On Tue, 1 Jan 2013, David Hartley wrote:
> Elliot <marsh@panix.com> writes

> > What more general definitions of Cech Stone compactifications are
> > there. Any beyond the construction with filters and the construction
> > for Tychonov T0 spaces?

>
> The one you referred to in your original post, i.e. in Wikipedia. Defined
> categorically in terms of the universal property and constructed using
> continuous functions into [0,1]. That's not always a compactification in the
> usual sense, which is why they added the comments which puzzled you.
>

Poof, all confusions banished. :-)