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...
The Rothberger property on
A space is said to have the Rothberger property (or simply is Rothberger) if for every sequence of open covers of , there exists for each such that . For any , necessary and sufficient conditions are obtained for to have the Rothberger property when is a Mrówka mad family and, assuming CH (the Continuum Hypothesis), we prove the existence of a maximal almost disjoint family for which the space is Rothberger for all .
The smallest ideals in the two natural products on ßS.
The Smirnov compactification as a quotient space of the Stone-Čech compactification.
The Sorgenfrey line has no connected compactification
The space of complete subgraphs of a graph
The star compactification.
The superextension of the closed unit interval is homeomorphic to the Hilbert cube
Three results on I-sets
Topological and Algebraic Copies of in .