# connectivity number

## connectivity number

[kə‚nek′tiv·əd·ē ‚nəm·bər]
(mathematics)
The number of points plus 1 which can be removed from a curve without separating the curve into more than one piece.
The number of closed cuts or cuts joining points of previous cuts (or joining points on the boundary) plus 1 which can be made on a surface without separating the surface. Also known as Betti number.
In general, the n-dimensional connectivity number of a topological space X is the number of infinite cyclic groups whose direct sum with the torsion group Gn (X) forms the homology group Hn (X).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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As the first step to study the problem of connectivity number of Fatou components in rational maps space with fixed degree, we just investigate the connectivity of any other Fatou component of R(z, t) as the real parameter t varies.
Stiemer, "Rational maps with Fatou components of arbitrary connectivity number," Computational Methods and Function Theory, vol.
It is practically invariant with the shape factor, as could be expected: as we already indicated in (Charollais et al., 1997), the connectivity properties of the Boolean model are invariant by affine transformations, which changes the shapes and the sizes, but does not introduce any new connection (this property was used to estimate the 3D connectivity number of a Boolean model of ellipsoids).
Other estimates of the percolation threshold are available: the excluded volume (Balberg et al., 1984), and the zeros of the connectivity number (Bretheau and Jeulin, 1989; Mecke and Stoyan, 2005), being only valid for isotropic Boolean models.
'Pakistan is a great market with very decent connectivity numbers. It's about providing customers with superior user experiences,' he said.
It was projected that the lack of legacy systems would lead to faster IPv6 deployment in the region, fueled by growing connectivity numbers and mobile network expansion.

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