nLab
simply connected space

Contents

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Definition

A simply connected topological space is a 1-connected topological space XX: a connected space whose fundamental group is the trivial group:

π 1(X)={e}\pi_1(X) = \{e\}.

Equivalently: if it is a simply connected object of the (∞,1)-topos Top.

See n-connected object of an (infinity,1)-topos for more.

Last revised on September 15, 2020 at 10:20:07. See the history of this page for a list of all contributions to it.