A natural mapping on a space of these objects named for Moore produces a fibration. These objects enjoy a locally unique homotopy lifting property. A space’s zeroth homology (-5[1])group counts components named for (-5[1])these objects, (-5[1])which are defined (-5[1])by a namesake (-5[1])form of connectedness. Equivalence (15[1])classes (15[2]-5[1])of these objects comprise (15[2])the (*) fundamental group. (10[2])A special case (-5[1])of the (10[1])max-cut min-flow theorem relates cut sets to sets of these objects, (-5[2])which are maps from the unit (-5[1])interval into a space. (10[2])Eulerian and Hamiltonian (10[1])examples (10[3])of these objects (10[4]-5[2])are (10[2])respectively sought by the Bridges of Königsberg (10[2]-5[1])and Traveling (10[1])Salesman problems. (10[1]-5[1])For 10 points, cycles are closed examples of what (10[1])sequences of edges (10[1])between (-5[1])two points (-5[1])on a graph? (0[1])■END■ (10[11]0[2])