Multiply connected space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

A topological space is said to be $n$-connected for a given $n\geq 0$ if its first $n$ homotopy groups are trivial. In particular:

• $0$-connected means path-connected space
• $1$-connected means simply connected space

A weakly contractible space is a topological space which is $n$-connected for every $n\geq 0$.