Mudcat Café Message Lyrics & Knowledge Personal Pages Record Shop Auction Links Radio & Media Kids Membership Help
The Mudcat Cafeawe



User Name Thread Name Subject Posted
Rapparee MOAB - Mother of All BS [annex] (2626* d) RE: MOAB - Mother of All BS [annex] 30 May 21


Don't worry about it as paracompact manifolds have all the topological properties of metric spaces. In particular, they are perfectly normal Hausdorff spaces. Manifolds are also commonly required to be second-countable. This is precisely the condition required to ensure that the manifold embeds in some finite-dimensional Euclidean space. However, non-Euclidean Hausdorff spaces do exist (probability approaches certainty) as the existence of manifolds in Hausdorff spaces includes non-Euclidean manifolds.


Post to this Thread -

Back to the Main Forum Page

By clicking on the User Name, you will requery the forum for that user. You will see everything that he or she has posted with that Mudcat name.

By clicking on the Thread Name, you will be sent to the Forum on that thread as if you selected it from the main Mudcat Forum page.
   * Click on the linked number with * to view the thread split into pages (click "d" for chronologically descending).

By clicking on the Subject, you will also go to the thread as if you selected it from the original Forum page, but also go directly to that particular message.

By clicking on the Date (Posted), you will dig out every message posted that day.

Try it all, you will see.