Cap

The symbol intersection , used for the intersection of sets, and sometimes also for the logical connective AND instead of the symbol ^ (wedge). In fact, for any two sets A and B

and this equivalence demonstrates the connection between the set-theoretical and the logical meaning.

The term "cap" is also used to refer to the topological object produced by puncturing a surface a single time, attaching two zips around the puncture in opposite directions, distorting the hole so that the zips line up, and then zipping up. The cap is topologically trivial in the sense that a surface with a cap is topologically equivalent to a surface without one.

See also

AND, Cross-Cap, Cross-Handle, Cup, Handle, Intersection, Spherical Cap, Wedge

Portions of this entry contributed by Margherita Barile

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References

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 2, 3rd ed. New York: Wiley, p. 104, 1971.Francis, G. K. and Weeks, J. R. "Conway's ZIP Proof." Amer. Math. Monthly 106, 393-399, 1999.

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Cap

Cite this as:

Barile, Margherita and Weisstein, Eric W. "Cap." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Cap.html

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