In the subject of
manifold theory in
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, if
is a
manifold with boundary, its double is obtained by gluing two copies of
together along their common boundary. Precisely, the double is
where
for all
.
Although the concept makes sense for any manifold, and even for some non-manifold sets such as the
Alexander horned sphere, the notion of double tends to be used primarily in the context that
is non-empty and
is
compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in Britis ...
.
Doubles bound
Given a manifold
, the double of
is the boundary of