Choose a point
and an
arbitrary point
then
there exists a path
between
and
in
. Indeed, assume
then the path-connectedness
of
implies the existence
of a path in
, which is also
a path in
. Similar for
. In the same manner we
obtain a path
between
and any other point
. Now, the concatenation
of path gives a path
from
(via
)
to
.