# Cell

A term sometimes used to denote a period parallelogram of a double-periodic function whose sides do not contain poles, and which is obtained from a fundamental period parallelogram by translation over a vector .

#### References

[1] | E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1927) |

#### Comments

In addition there are several technical meanings of the word cell in geometry and topology. Thus, in affine geometry the convex hull of a finite set of points is sometimes called a convex cell. A subset of a topological Hausdorff space such that there is a relative homeomorphism is a (topological) -dimensional cell. Here is the unit ball, its boundary is the -dimensional sphere, and a relative homeomorphism is, of course, a continuous mapping such that and induces a homeomorphism ; cf. also Cell complex and Cellular space. The phrase unit cell occasionally occurs as a synonym for the ball (disc) of radius one centred at the origin in -dimensional Euclidean space, and any space homeomorphic to it is also sometimes called an -dimensional topological cell. Finally, cell is sometimes used to denote the possible locations of entries in a matrix or similar structure, such as a magic square or Young diagram, or as a synonym for a block in a block matrix.

**How to Cite This Entry:**

Cell.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Cell&oldid=15623