Cover

cover

1. woods or bushes providing shelter or a habitat for wild creatures

2. 

a. a blanket used on a bed for warmth

b. another word for bedspread

3. Philately

a. an entire envelope that has been postmarked

b. on cover (of a postage stamp) kept in this form by collectors

4. Pop music a version by a different artist of a previously recorded musical item

5. Cricket

a. the area more or less at right angles to the pitch on the off side and usually about halfway to the boundary

b. (as modifier): a cover drive by a batsman

c. a fielder in such a position

6. Ecology the percentage of the ground surface covered by a given species of plant

7. break cover (esp of game animals) to come out from a shelter or hiding place

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cover [′kəv·ər]

(mathematics)

An element,x, of a partially ordered set covers another elementyifxis greater thany, and the only elements that are both greater than or equal toyand less than or equal toxarexandythemselves.

also covering

(mining engineering)

The thickness of rock between the mine workings and the surface.

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cover

1. In reinforced concrete, the least distance between the surface of the reinforcement and the outer surface of the concrete.

2. That part of a tile or shingle which is covered by the next course.

3. The concrete (or concrete-like material) which covers steel reinforcement to protect the steel from possible fire damage or corrosion.

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Cover 

(or covering), a collection of point sets (geometric figures) whose union forms or contains a given set (or given figure). For example, the diagonal of a rectangle divides it into two triangles that form a cover of the given rectangle. Finite covers—that is, covers consisting of a finite number of elements —are usually considered. If the diameter of each of the sets of a cover is smaller than a given positive ∊, the cover is called an ∊-cover.

For any ∊ > 0, a bounded region permits of a finite ∊-cover by closed sets with at most three sets intersecting at a time, but it permits of no such cover, for a sufficiently small ∊, with only two sets intersecting at a time. Thus, a town square can be covered with arbitrarily small paving blocks in such a way that the stones in the pavement will border only in threes; borderings in threes cannot be avoided. Similarly, when a space is filled with brickwork, the bricks can be made to border only in fours; the borderings cannot be only in threes. Hence, the importance of the concept of the multiplicity of a cover. We say that the multiplicity of a cover of a given set does not exceed n if every point of the set belongs to no more than n sets of the cover. Thus, the multiplicity of finite covers makes it possible to characterize the number of dimensions of a space. In topology, covers are a powerful means of investigating various geometric properties of sets.

P. S. ALEKSANDROV