# bundle

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## bundle

**1.**

*Biology*a collection of strands of specialized tissue such as nerve fibres

**3.**

*Textiles*a measure of yarn or cloth; 60 000 yards of linen yarn; 5 or 10 pounds of cotton hanks

## Bundle

in mathematics, a two-parameter family of curves in the plane or in space that are linear functions of the parameters. Suppose *F*_{1}, *F*_{2}, and *F*_{3} are functions of two variables and none of the functions is a linear combination of the other two. The family of curves in the plane that are determined by the equation

(*) λ_{1}*F*_{1} + λ_{2}*F*_{2} + λ_{3}*F*_{3} = 0

for all possible values of the parameters λ_{1}, λ_{2}, and λ_{3} (except for the case λ_{1} = 0, λ_{2} = 0, and λ_{3} = 0) constitutes a bundle. Equation (*) is in fact a function of two parameters—that is, of the two ratios λ_{1}: λ_{2}: λ_{3}. In addition, it is immediately apparent that the parameters occur in this equation linearly. The equation of a bundle of surfaces in space is formed analogously. The three equations *F*_{1} = 0, *F*_{2} = 0, and *F*_{3} = 0 yield three elements of the bundle (three curves of three surfaces), which determine the entire bundle.

Bundles are usually considered whose elements are similar in certain respects; examples are a bundle of circles and a bundle of planes. We sometimes also speak of a bundle of lines in space; although the bundle is considered in space, its elements are curves rather than surfaces. Nevertheless, this case can be reduced to the case of a bundle of planes, since the pairwise intersections of elements of a bundle of planes determine a set of lines. In projective geometry, a bundle is understood to mean both sets—lines and planes—at once.

## bundle

[′bən·dəl]*E*,

*p*,

*B*), where

*E*and

*B*are topological spaces and

*p*is a continuous map of

*E*onto

*B*; intuitively

*E*is the collection of inverse images under

*p*of points from

*B*glued together by the topology of

*X*.

## bundle

**(1)**To sell hardware and software as a combined product or to combine several software packages for sale as a single unit. Contrast with unbundle. See bundled software and bundling.

**(2)**A collection of files that are treated as one. See APP file.