Convex Set is Simply Connected

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Let $\struct {V, \tau}$ be a topological vector space over $\R$ or $\C$.

Let $A \subseteq V$ be a non-empty convex set.

Let $\tau_A$ be the subspace topology on $A$ induced by $\tau$.

Then $\struct{ A, \tau_A }$ is simply connected.


Follows from Convex Set is Star Convex Set and Star Convex Set is Simply Connected.