The general notion of topology does not allow to compare neighborhoods of different points. Such a comparison is quite natural in various geometric contexts. The general setting for such a comparison is that of a uniform structure. The most common and natural way for a uniform structure to appear is via a metric, which was already mentioned on several occasions in Chapter 1, so we will postpone...

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

recently, data collection from seabed by means of underwater wireless sensor networks (uwsn) has attracted considerable attention. autonomous underwater vehicles (auvs) are increasingly used as uwsns in underwater missions. events and environmental parameters in underwater regions have a stochastic nature. the target area must be covered by sensors to observe and report events. a ‘topology cont...

Random Boolean networks (RBNs) were first introduced and used to model regulatory gene networks by Kauffman in 1969 and since then have been frequently used to model networks at various levels of biological organization. The standard model has a characteristic topology in which the network has N genes with an average of K input connections selected at random. We have used RBNs to examine regula...

The two main results in this paper are analogues of the Stone-Weierstrass theorem for real-valued functions, obtained by using different function space topologies. The first (Theorem 2.3) is a Stone-Weierstrass theorem for unbounded functions. The second (Theorem 3.6) is a theorem for bounded functions ; it is stronger than the usual theorem because the topology is larger than the uniform topol...

We characterize the compactness properties of the product of λ copies of the space ω with the discrete topology, dealing in particular with the case λ singular, using regular and uniform ultrafilters, infinitary languages and nonstandard elements. We also deal with products of uncountable regular cardinals with the order topology. 2010 Mathematics Subject Classification 54B10, 54D20, 03C75 (pri...

We prove that if D ⊂ Cn is a bounded domain with real analytic boundary, and D is either pseudoconvex or it satisfies condition R, then the the compact open topology in Aut (D), the group of holomorphic automorphisms of D is the the topology of uniform convergence on D.