nLab simply connected space

Redirected from "simply-connected topological spaces".
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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

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Paths and cylinders

Homotopy groups

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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) = \{\mathrm{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 July 16, 2022 at 21:15:03. See the history of this page for a list of all contributions to it.