Theorem
The union of two continua with a common point is a continuum.
Proof
Letand
be compact connected spaces with a point
in common so
is compact.
Sinceand
are connected with a common point,
is connected.
Henceis a continuum.
Theorem
The union of two continua with a common point is a continuum.
Proof
Letand
be compact connected spaces with a point
in common so
is compact.
Sinceand
are connected with a common point,
is connected.
Henceis a continuum.