A Boolean view of sequential compactness
A characterization of Corson-compact spaces
We characterize Corson-compact spaces by means of countable elementary substructures.
A characterization of movable compacta.
A characterization of pseudocompactness.
A characterization of Valdivia compact spaces.
A classification of H-closed extensions
A classification of separable Rosenthal compacta and its applications [Book]
A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom
We answer a question of I. Juhasz by showing that MA CH does not imply that every compact ccc space of countable -character is separable. The space constructed has the additional property that it does not map continuously onto .
A compact Fréchet space whose square is not Fréchet
A compact Hausdorff topology that is a T₁-complement of itself
Topologies τ₁ and τ₂ on a set X are called T₁-complementary if τ₁ ∩ τ₂ = X∖F: F ⊆ X is finite ∪ ∅ and τ₁∪τ₂ is a subbase for the discrete topology on X. Topological spaces and are called T₁-complementary provided that there exists a bijection f: X → Y such that and are T₁-complementary topologies on X. We provide an example of a compact Hausdorff space of size which is T₁-complementary to itself ( denotes the cardinality of the continuum). We prove that the existence of a compact Hausdorff...
A compactness result in thin-film micromagnetics and the optimality of the Néel wall
In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for -valued maps (the magnetization) of two variables : . We are interested in the behavior of minimizers as . They are expected to be -valued maps of vanishing distributional divergence , so that appropriate boundary conditions enforce line discontinuities. For finite , these line discontinuities are approximated by smooth transition layers, the so-called Néel walls. Néel...
A constructive proof of the Tychonoff's theorem for locales
A Corson compact L-space from a Suslin tree
The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.
A decomposition theorem for compact groups with an application to supercompactness
We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.
A first countable supercompact Hausdorff space with a closed nonsupercompact subspace
A general invariant metrization theorem for compact spaces
A generalisation of almost-compactness, with an associated generalisation of completeness
A Generalization of Chain-net Spaces
A generalization of -compact spaces
A generalization of Magill's Theorem for non-locally compact spaces
In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the...