More generally, one can define the fundamental groupoid on any subset of using homotopy classes of paths joining points of This is convenient for the Van Kampen's Theorem. See also Path space (disambiguation) References Ronald Brown, Topology and groupoids, Booksurge PLC, (2006). J. Peter May, A concise course in algebraic topology, University of Chicago Press, (1999). James Munkres, Topology 2ed, Prentice Hall, (2000). Topology Homotopy theory