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Two subspaces S_1 and S_2 of R^n are said to be orthogonal if the dot product v_1·v_2=0 for all vectors v_1 in S_1 and all v_2 in S_2.

A braid in which strands are intertwined in the center and are free in "handles" on either side of the diagram.

A type II Markov move.

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

Let Y^X be the set of continuous mappings f:X->Y. Then the topological space Y^X supplied with the compact-open topology is called a mapping space. If (Y,*) is a pointed ...

A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

Let X and Y be CW-complexes and let X_n (respectively Y_n) denote the n-skeleton of X (respectively Y). Then a continuous map f:X->Y is said to be cellular if it takes ...

A subset of a topological space which is compact with respect to the relative topology.