Une structure uniforme sur un espace
The Brouwer’s plane translation theorem asserts that for a fixed point free orientation preserving homeomorphism f of the plane, every point belongs to a Brouwer line: a proper topological embedding C of R, disjoint from its image and separating f(C) and f–1(C). Suppose that f commutes with the elements of a discrete group G of orientation preserving homeomorphisms acting freely and properly on the plane. We will construct a G-invariant topological foliation of the plane by Brouwer lines. We apply...
For a completely regular space X, C(X) and C*(X) denote, respectively, the algebra of all real-valued continuous functions and bounded real-valued continuous functions over X. When X is not a pseudocompact space, i.e., if C*(X) ≠ C(X), theorems about uniform density for subsets of C*(X) are not directly translatable to C(X). In [1], Anderson gives a sufficient condition in order for certain rings of C(X) to be uniformly dense, but this condition is not necessary.In this paper we study the uniform...