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In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below. A topological space is a 3-manifold if it is a second-countable Hausdorff space and if every point in has a neighbourhood that is homeomorphic to Euclidean 3-space.
This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric topology. All spaces in this glossary are assumed to be topological spaces unless stated otherwise. Absolutely closed See H-closed Accessible See . Accumulation point See limit point.
This is a list of geometric topology topics. List of mathematical knots and links Knot (mathematics) Link (knot theory) Wild knots Examples of knots Unknot Trefoil knot Figure-eight knot (mathematics) Borromean rings Types of knots Torus knot Prime knot Alternating knot Hyperbolic link Knot invariants Crossing number Linking number Skein relation Knot polynomials Alexander polynomial Jones polynomial Knot group Writhe Quandle Seifert surface Braids Braid theory Braid group Kirby calculus Genus (mathematics