Theorem
A componentof a locally connected space
is open.
Proof
Letbe a component of a locally connected space
and let
Sinceis locally connected, a belongs to at least one open connected set
and since each
is open, so is
Theorem
A componentof a locally connected space
is open.
Proof
Letbe a component of a locally connected space
and let
Sinceis locally connected, a belongs to at least one open connected set
and since each
is open, so is