In
topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
, a branch of mathematics, an excisive triad is a triple
of
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...
s such that ''A'', ''B'' are subspaces of ''X'' and ''X'' is the union of the interior of ''A'' and the interior of ''B''.
Note ''B'' is not required to be a
subspace of ''A''.
See also
*
Homotopy excision theorem
In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let (X; A, B) be an excisive triad with C = A \cap B nonempty, and suppose the pair (A, C) is (m-1)-connect ...
Notes
References
*
*
Munkres, James; ''Topology'', Prentice Hall; 2nd edition (December 28, 1999). .
{{topology-stub
Topology
General topology