-frames and almost compact frames
-catégories (catégories dans un triple)
-spaces and the Wallman compactification.
Tensor products with bounded continuous functions.
The Banach algebra of continuous bounded functions with separable support
We prove a commutative Gelfand-Naimark type theorem, by showing that the set of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...
The category of compactifications and its coreflections
We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone . A corCM implies the assignment to each locally compact, noncompact a compactification minimum for membership in the “object-range” of . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...
The classes of mutual compactificability.
The compactificability classes of certain spaces.
The compactificability classes: The behavior at infinity.
The dimension of remainders of rim-compact spaces
Answering a question of Isbell we show that there exists a rim-compact space X such that every compactification Y of X has dim(Y)≥ 1.
The Fermi surface for the discretized Maxwell equations
The Freudenthal compactification [Book]
The Haar measure of certain sets in the Bohr group
The -compactification of a topologized semigroup
The minimal ideals of a multiplicative and additive subsemigroup of ßN.
The minimum uniform compactification of a metric space
It is shown that associated with each metric space (X,d) there is a compactification of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of are presented, and a detailed study of the structure of is undertaken. This culminates in a topological characterization of the outgrowth , where is Euclidean n-space with its usual metric.
The Nachbin compactification via convergence ordered spaces.
The notions of w-net and Y-compact space viewed under infinitesimal microscope.
The one-point countable compactification of curve spaces and arc spaces
The partially pre-ordered set of compactifications of Cp(X, Y)
In the set of compactifications of X we consider the partial pre-order defined by (W, h) ≤X (Z, g) if there is a continuous function f : Z ⇢ W, such that (f ∘ g)(x) = h(x) for every x ∈ X. Two elements (W, h) and (Z, g) of K(X) are equivalent, (W, h) ≡X (Z, g), if there is a homeomorphism h : W ! Z such that (f ∘ g)(x) = h(x) for every x ∈ X. We denote by K(X) the upper semilattice of classes of equivalence of compactifications of X defined by ≤X and ≡X. We analyze in this article K(Cp(X, Y)) where...