# closed ball

## closed ball

[¦klōzd ′bȯl]
(mathematics)
In a metric space, a closed set about a point x which consists of all points that are equal to or less than a fixed distance from x.
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That makes it possible for him to deposit 1.8 million liters of pig waste in the biodigester, a large closed ball of black canvas, half buried in a pit measuring about 10 meters in diameter, where it ferments, thanks to anaerobic bacteria.
, discussed the result related to [[alpha].sub.*]-[psi]-Ciric type multivalued mappings on an intersection of a closed ball and a sequence with graph.
Thus the mappings [??] and [??] satisfy all the conditions of Theorem 12 on closed ball rather than on whole space.
* The norm closed ball B(H)[[parallel]*[parallel].sub.[less than or equal to]n], centered at 0 with radius n, is closed under topologies [tau]'s.
An open ball is usually denoted by B(r), and closed ball is denoted by [bar.B](r), where
Let BX denote the closed unit ball of X and B(x, r) denote the closed ball with center at x [member of] X and radius r > 0.
The intersection of [??] with the projective half-space [[??].sup.-.sub.x] = {x' [member of] PV | B(x, x') [less than or equal to] 0} is a closed ball (spherical cap) on [??].
The closed ball [[bar.B].sub.N](v, r, i) with center x, radius r, 0 < r < 1, and i > 0 is defined as follows:
Let us assume that for every closed ball B [subset] X there exists N with B [subset or equal to] [X.sub.n] for every n [greater than or equal to] N and [[lambda].sub.n] converges to [lambda] uniformly in B.
in some closed ball which contains {[x.sub.n]}, then [x.sup.*] is a solution of F(x) = 0.
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] define as above, and B be any closed ball in [R.sup.n] large enough to ensure that [w.sub.i](B) [subset or equal to]] B, i = (1, 2, ..., m).

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