Path-connected space

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A topological space is path-connected if for every pair $x,y\in X$ , there is a path $\gamma:[0,1]\rightarrow X$ whose endpoints are $x$ and $y$ .

Practice this concept with exercises

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Soit $X$ un espace topologique.
Soit $A$ et $B$ , deux parties connexes par arcs tel que $A\cap B\neq \emptyset$ .
Montrez que $A\cup B$ est connexe par arcs.

Open exercise

Problems using this concept (3)

\mathrm{GL}_n(\mathbb{R})

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