Double mapping cylinder
From Topospaces
Definition
Suppose are topological spaces and
and
are continuous maps. The double mapping cylinder of
and
is defined as the quotient of
via the relations
and
.
Particular cases
- Mapping cylinder: Here
and
is the identity map
- Mapping cone: Here
is a one-point space and
is the map to that one point
- Join: The join of spaces
and
is the double mapping cylinder where
,
,
and the maps are simply projections onto the coordinates