Let X be a compact Hausdorff space and M a metric space. E0(X,M) is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which E0(X,M) is all of C(X,M). These include βN\N, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case thatM is...

LetH∞ be the Banach algebra of all bounded analytic functions in the unit disk D. A function f ∈ H∞ is said to be universal with respect to the sequence ( z+zn 1+znz )n of noneuclidian translates, if the set {f( z+zn 1+znz ) : n ∈ N} is locally uniformly dense in the set of all holomorphic functions bounded by ||f ||∞. We show that for any sequence of points (zn) in D tending to the boundary th...

The problem of styling surfaces modeling is tackled. An approach based on section curves fairing is chosen. The concept of template curves is developed for approximating profiles with a monotone curvature variation. Constrained Bezier curves called typical curves are used for that. A curve growing process based on a G typical curve fitting method, is investigated. It consists first in determini...

Real-world applications now deal with a massive amount of data, and information about the world is inaccurate, incomplete, or uncertain. Therefore, we present in our paper proposed model for solving problems. This based on class locally generalized closed sets, namely, simply* alpha closed* sets closed** (briefly, -sets -sets), open set. We also introduce various concepts their properties relat...