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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 ...

A totally imaginary field is a field with no real embeddings. A general number field K of degree n has s real embeddings (0<=s<=n) and 2t imaginary embeddings (0<=t<=n/2), ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A square matrix is said to be totally positive if the determinant of any square submatrix, including the minors, is positive. For instance, any 2×2 matrix whose determinant ...

A plane partition which is invariant under permutation of the three axes and which is equal to its complement (i.e., the collection of cubes that are in a given box but do ...

A totative is a positive integer less than or equal to a number n which is also relatively prime to n, where 1 is counted as being relatively prime to all numbers. The number ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

N_phi(m) is the number of integers n for which the totient function phi(n)=m, also called the multiplicity of m (Guy 1994). Erdős (1958) proved that if a multiplicity occurs ...

B_(p+k)=B_k+B_(k+1) (mod p), when p is prime and B_n is a Bell number.