Basic Algebraic Topology and its Applications by Mahima Ranjan Adhikari

Author:Mahima Ranjan Adhikari
Language: eng
Format: epub, pdf
Publisher: Springer India, New Delhi

This definition is generalized for (X, A) in .

Definition 7.12.2

For any pair of topological spaces (X, A) in , the nth-cohomotopy set is defined to be the set of all homotopy classes relative to A of continuous maps . In particular, if is defined by and called the n th-cohomotopy set of the topological space X.

Remark 7.12.3

has a distinguished element namely, the homotopy class of the constant map . The element [c] is denoted by the symbol 0 and called the zero element of .

Definition 7.12.4

is defined to be the set of all open and closed subspaces of X not intersecting A. The zero element of is the empty subspace of X.

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