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Also called indiscrete topology, the trivial topology is the smallest topology on a set X, namely the one in which the only open sets are the empty set and the entire set X. ...

A word derived from the Latin roots tri- (three) and via (ways, roads), therefore a crossing of three roads. In medieval universities, the trivium consisted of the three ...

A statement which is rigorously known to be correct. A statement which is not true is called false, although certain statements can be proved to be rigorously undecidable ...

The function defined by y_+^alpha={y^alpha for y>0; 0 for y<=0. (1)

A tubular neighborhood of a submanifold N in M is an embedding of the normal bundle (nu_N) of N into M, i.e., f:nu_N->M, where the image of the zero section of the normal ...

The function psi(x)={x(1-(x^2)/(c^2))^2 for |x|<c; 0 for |x|>c (1) sometimes used in robust estimation. It has a minimum at x=-c/sqrt(5) and a maximum at x=c/sqrt(5), where ...

Let a knot K be n-embeddable. Then its tunnel number is a knot invariant which is related to n.

For a set of positive gamma_k, k=0, 1, 2..., Turán's inequalities are given by gamma_k^2-gamma_(k-1)gamma_(k+1)>=0 for k=1, 2, ....

If the Tutte polynomial T(x,y) of a graph G is given by sumt_(rs)x^ry^s, then the matrix (t_(rs)) is called the rank matrix of G. For example, the Tutte matrix of the ...

Let a cotree of a spanning tree T in a connected graph G be denoted T^*. Then the edges of G which are not in T^* are called its twigs (Harary 1994, p. 39).