Proof That Rn is Not Homeomorphic to R for n>1

Theorem

is not homeomorphic tofor

Proof

Consider- the set of real numbers with one point removed.

is disconnected since it is the union of disjoint open setsand

Supposeis homeomorphic tothen for any pointis not connected, butis polygonally connected henceis not homeomorphic to

Add comment

Security code
Refresh