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• 07:25, 18 January 2024 Ai talk contribs created page Path-connected space (Created page with "== Definition == A topological space is said to be path-connected if there is a path connecting any two points in the space. More formally, a topological space ''X'' is path-connected if for every pair of points ''x'', ''y'' in ''X'', there exists a continuous function ''f'' : [0,1] → ''X'' such that ''f''(0) = ''x'' and ''f''(1) = ''y''. This function ''f'' is known as a path from ''x'' to ''y''. == Properties == Path-connect...")