🚀 go-pugleaf

In article <1992Nov5.004804.24757@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

)I guess you may have the basic gut idea of a manifold, since you
)referred to Lobachevsky.  Anyway, the idea is that a manifold is a
)generalization of a surface to higher dimensions.  

A rash assumption!  I've picked up some of an idea from the net, however.

I should mention that if you like mathematics and sarcastic humor, you
could do a lot worse than pick up some of the songs by Tom Leher.
"Lobachevsky" is one of his songs.

In it, the main character of the song (who is Russian, of course) offers
the following advice, in a thick russian accent and with fractured syntax.

"Plagarize, Plagarize, Plagarize!  Only be sure to always call it - 
research"

Leher, a mathematics professor turned songwriter/performer,  wrote other very
nice sarcastic parodies, a fair number of which have some mathematical and/or
scientific content (not all do, however), including the "Hunting Song",
"Werner Von Braun", "National Brotherhood Week", "The New Math", and "The
Elements". Leher is just as much (if not more) fun than reading usenet!

)Anyway, manifolds come in several flavors, most notably "smooth" and
)"topological".  A topological manifold is a Hausdorff space such that every
)point has a neighborhood homeomorphic to R^n (Euclidean n-space).  Now
)you should ask me to define whatever didn't make any sense in that
)definition!

What's a Hausdorff space?  For that matter, what's homeomorphic? (one-to
one reversible mapping??).