#
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 $X$: a connected space whose fundamental group is the trivial group:

$\pi_1(X) = \{e\}$.

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.
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