"Ronn!Blankenship" wrote:
...
> >I'm too sophomoric to bother to read.
>
> "A is homeomorphic to B" means that there is a homeomorphism which maps A
> to B. A homeomorphism is a bicontinuous bijection.
A bijection is a function that is one-to-one and onto.
A function is a particular kind of set of ordered pairs.
A function is one-to-one iff ...
I have a vision of producing a "definition tree" for
the word homeomorphism, which I'll write as an outline:
homeomorphism
bicontinuous
continuous
open set (undefined term)
inverse image
inverse
bijection
one-to-one
image
onto
image (O.K., so it's not a tree...)
function
Cartesian product
ordered pair (undefined?)
And I'm sure I left some stuff out.
---David
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