[{"n": "Topological space", "u": "/e/part-1/topological-space/", "s": "A set with structure defining closeness without distance."}, {"n": "Topology", "u": "/e/part-1/topology/", "s": "Study of properties preserved under continuous deformations."}, {"n": "Sheaf (mathematics)", "u": "/e/part-1/sheaf-mathematics/", "s": "Tool for tracking local data on topological spaces."}, {"n": "Surface (topology)", "u": "/e/part-1/surface-topology/", "s": "A surface is a two-dimensional topological manifold."}, {"n": "Systolic geometry", "u": "/e/part-1/systolic-geometry/", "s": "Study of least-length noncontractible loops in manifolds and polyhedra."}, {"n": "Winding number", "u": "/e/part-1/winding-number/", "s": "Integer count of a curve's counterclockwise turns around a point."}, {"n": "Homotopy", "u": "/e/part-1/homotopy/", "s": "A continuous deformation between two functions in topology."}, {"n": "Fundamental group", "u": "/e/part-1/fundamental-group/", "s": "A homotopy invariant group of loops in a topological space."}, {"n": "Manifold", "u": "/e/part-1/manifold/", "s": "A topological space locally resembling Euclidean space near each point."}, {"n": "Covering space", "u": "/e/part-1/covering-space/", "s": "A space that locally projects multiple copies onto a base space."}, {"n": "Betti number", "u": "/e/part-1/betti-number/", "s": "Topological invariants measuring holes in spaces."}, {"n": "Euler characteristic", "u": "/e/part-1/euler-characteristic/", "s": "Topological invariant describing shape regardless of bending."}, {"n": "Möbius strip", "u": "/e/part-1/m-bius-strip/", "s": "A non-orientable surface with one side and one boundary."}, {"n": "Klein bottle", "u": "/e/part-1/klein-bottle/", "s": "A one-sided surface with no boundary."}, {"n": "Compact space", "u": "/e/part-1/compact-space/", "s": "A topological property making spaces behave like finite sets."}]