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Let X be a Riemann surface.Then the intersection number of two closed curves on X has a simple definition in terms of an integral. For every closed curve c on X (i.e., smooth function :), we can associate a differential form of compact support, the Poincaré dual of c, with the property that integrals along c can be calculated by integrals over X:
As well as being called the intersection number, the minimum number of these cliques has been called the R-content, [7] edge clique cover number, [4] or clique cover number. [8] The problem of computing the intersection number has been called the intersection number problem , [ 9 ] the intersection graph basis problem , [ 10 ] covering by ...
In terms of intersection forms, we say the plane has one of type x 2 (there is only one class of lines, and they all intersect with each other). Note that on the affine plane, one might push off L to a parallel line, so (thinking geometrically) the number of intersection points depends on the choice of push-off. One says that “the affine ...
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As another example, the number 5 is not contained in the intersection of the set of prime numbers {2, 3, 5, 7, 11, …} and the set of even numbers {2, 4, 6, 8, 10, …} , because although 5 is a prime number, it is not even. In fact, the number 2 is the only number in the intersection of these two
Let be a set and a nonempty family of subsets of ; that is, is a nonempty subset of the power set of . Then is said to have the finite intersection property if every nonempty finite subfamily has nonempty intersection; it is said to have the strong finite intersection property if that intersection is always infinite.
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This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. Mathematics Wikipedia:WikiProject Mathematics Template:WikiProject Mathematics ...