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A subset of a topological space is called clopen if it is both closed and open.

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

The look and say sequence generated from a starting digit of 3, as given by Vardi (1991).

The cotangent function cotz is the function defined by cotz = 1/(tanz) (1) = (i(e^(iz)+e^(-iz)))/(e^(iz)-e^(-iz)) (2) = (i(e^(2iz)+1))/(e^(2iz)-1), (3) where tanz is the ...

R_m(x,y) = (J_m^'(x)Y_m^'(y)-J_m^'(y)Y_m^'(x))/(J_m(x)Y_m^'(y)-J_m^'(y)Y_m(x)) (1) S_m(x,y) = (J_m^'(x)Y_m(y)-J_m(y)Y_m^'(x))/(J_m(x)Y_m(y)-J_m(y)Y_m(x)). (2)

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

Two cones placed apex to apex. The double cone is given by algebraic equation (z^2)/(c^2)=(x^2+y^2)/(a^2).