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An H-space, named after Heinz Hopf, and sometimes also called a Hopf space, is a topological space together with a continuous binary operation mu:X×X->X, such that there ...

A topological space fulfilling the T3-separation axiom: X fulfils the T1-separation axiom and is regular. According to the terminology of Alexandroff and Hopf (1972), ...

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

A topological space fulfilling the T_2-axiom: i.e., any two points have disjoint neighborhoods. In the terminology of Alexandroff and Hopf (1972), a T_2-space is called a ...

A braid index is the least number of strings needed to make a closed braid representation of a link. The braid index is equal to the least number of Seifert circles in any ...

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...

The unlink, also called the trivial link, of n components consist of n disjoint circles in a plane (Rolfsen 1976, p. 65).

A T_1-space is a topological space fulfilling the T1-separation axiom: For any two points x,y in X there exists two open sets U and V such that x in U and y not in U, and y ...

A single component algebraic link. Most knots up to 11 crossings are algebraic, but they quickly become outnumbered by nonalgebraic knots for more crossings (Hoste et al. ...