path components functor

 topology
Notation π0:Top→Set\pi_0: \Top \to \Set Domain category of topological spacesCodomain category of sets Related UTopU_{\Top}, π1\pi_1 External nLab Link

This functor maps a topological space XX to its set π0(X)\pi_0(X) of path components. Thus, π0(X)=U(X)/∼\pi_0(X) = U(X) / {\sim}, where U(X)U(X) is the underlying set and x∼yx \sim y when there is a path from xx to yy.

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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