# cover

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## cover

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

**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

## Cover

## 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

## cover

[′kəv·ər]*x*, of a partially ordered set covers another element

*y*if

*x*is greater than

*y*, and the only elements that are both greater than or equal to

*y*and less than or equal to

*x*are

*x*and

*y*themselves.

**also covering**

## 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.

## cover

**i**. An area on the ground covered by imagery, photograph, mosaic, etc.

**ii**. The protection of friendly forces (ground, maritime, or air) by friendly aircraft and/or by EW (electronic warfare) aircraft.

**iii**. That which conceals or protects, such as darkness, a topographical feature, a bank of clouds, a shell barrage, or a deceptive move.