Proof That Any Connected Subset of a Set Consisting of Disjoint Open Subsets Must be Contained in One of Those Subsets


Supposeis a space such thatwhereandare nonempty, open subsets of

Ifis any connected subset ofthen eitheror


Supposewithand thatand

Thenare nonempty, disjoint, subsets ofopen inand

Henceis not connected and eitherorhence eitheror

You have no rights to post comments