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Let A={A_1,A_2,...,A_n} be a union-closed set, then the union-closed set conjecture states that an element exists which belongs to at least n/2 of the sets in A. Sarvate and ...

In the theory of transfinite ordinal numbers, 1. Every well ordered set has a unique ordinal number, 2. Every segment of ordinals (i.e., any set of ordinals arranged in ...

Let L be a language of the first-order logic. Assume that the language L has the following sets of nonlogical symbols: 1. C is the set of constant symbols of L. (These are ...

A Tychonoff plank is a topological space that is an example of a normal space which has a non-normal subset, thus showing that normality is not a hereditary property. Let ...

Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...

A conclusion is a statement arrived at by applying a set of logical rules known as syllogisms to a set of premises. The process of drawing conclusions from premises and ...

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...