Definition:Contractible Space/Definition 2

Definition

Let $X$ be a topological space.

$X$ is called contractible if and only if it is homotopy equivalent to a point.

Also see

• Equivalence of Definitions of Contractible Space

• Results about contractible spaces can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): contractible
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): homotopy
• 2001: Allen Hatcher: Algebraic Topology: $0$: Some Underlying Geometric Notions: Homotopy and Homotopy Type
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): contractible
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): homotopy
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): contractible space