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The quartic surface given by the equation x^4+y^4+z^4-(x^2+y^2+z^2)=0.

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

Two maps phi,psi:M->M are said to be topologically conjugate if there exists a homeomorphism h:M->M such that phi degreesh=h degreespsi, i.e., h maps psi-orbits onto ...

A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

A ring torus constructed out of a square of side length c can be dissected into two squares of arbitrary side lengths a and b (as long as they are consistent with the size of ...

If one part of the total intersection group of a curve of order n with a curve of order n_1+n_2 constitutes the total intersection with a curve of order n_1, then the other ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

The space E of a fiber bundle given by the map f:E->B, where B is the base space of the fiber bundle.

A totally disconnected space is a space in which all subsets with more than one element are disconnected. In particular, if it has more than one element, it is a disconnected ...