Timeline for The Alexandroff compactification is the biggest one-point compactification?

8 events

when toggle format	what		by	license	comment
Oct 23, 2012 at 23:25	comment	added	Camilo Arosemena Serrato		sorry, I hadn't seen your "moreover"
Oct 23, 2012 at 21:57	comment	added	Brian M. Scott		@Camilo: My statement that $\tau^$ and $\tau'$ have the same nbhds of $p$ means exactly the same as your version. And yes, we do necessarily have $\tau^\subseteq\tau'$; what my example shows is that we don’t necessarily have $\tau'\subseteq\tau^*$.
Oct 23, 2012 at 21:47	comment	added	Camilo Arosemena Serrato		and also think that what you wanted to show in the first part was that $p$ has the same neighborhoods in $\left<{X,\tau^´}\right>$ and $\left<{X,\tau^}\right>$; note that not necessarly we have $\tau^\subseteq{\tau^´}$, because of your counterexamnple; note that the space of your counterexample is locally compact.
Oct 23, 2012 at 21:40	vote	accept	Camilo Arosemena Serrato
Oct 23, 2012 at 21:39	comment	added	Brian M. Scott		@Camilo: I did indeed; thanks for catching it.
Oct 23, 2012 at 21:39	history	edited	Brian M. Scott	CC BY-SA 3.0	Fixed a typo.
Oct 23, 2012 at 21:34	comment	added	Camilo Arosemena Serrato		I think what you meant was $\left\{{0}\right\}\cup{\left\{{\displaystyle\frac{1}{n}:n\in{\mathbb{Z}^+}}\right\}}$, correcting this your proof, is correct Thank you very much!!!!!!!!
Oct 23, 2012 at 7:04	history	answered	Brian M. Scott	CC BY-SA 3.0