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We answer a question of I. Juhasz by showing that MA $+ \neg$ CH does not imply that every compact ccc space of countable $π$ -character is separable. The space constructed has the additional property that it does not map continuously onto $I^{ω_{1}}$ .

A compact Fréchet space whose square is not Fréchet

Petr Simon (1980)

Commentationes Mathematicae Universitatis Carolinae

A compact Hausdorff topology that is a T₁-complement of itself

Dmitri Shakhmatov, Michael Tkachenko (2002)

Fundamenta Mathematicae

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 $(X, τ_{X})$ and $(Y, τ_{Y})$ are called T₁-complementary provided that there exists a bijection f: X → Y such that $τ_{X}$ and $f^{- 1} (U) : U \in τ_{Y}$ are T₁-complementary topologies on X. We provide an example of a compact Hausdorff space of size $2^{}$ 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

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for $S^{1}$ -valued maps $m^{'}$ (the magnetization) of two variables $x^{'}$ : $E_{ε} (m^{'}) = ε \int {| \nabla^{'} \cdot m^{'} |}^{2} d x^{'} + \frac{1}{2} \int {|| \nabla^{'} |^{- 1 / 2} \nabla^{'} \cdot m^{'}|}^{2} d x^{'}$ . We are interested in the behavior of minimizers as $ε \to 0$ . They are expected to be $S^{1}$ -valued maps $m^{'}$ of vanishing distributional divergence $\nabla^{'} \cdot m^{'} = 0$ , so that appropriate boundary conditions enforce line discontinuities. For finite $ε > 0$ , 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

Igor Kříž (1985)

Commentationes Mathematicae Universitatis Carolinae

A Corson compact L-space from a Suslin tree

Peter Nyikos (2015)

Colloquium Mathematicae

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 countably cellular topological group all of whose countable subsets are closed need not be $ℝ$ -factorizable

Mihail G. Tkachenko (2023)

Commentationes Mathematicae Universitatis Carolinae

We construct a Hausdorff topological group $G$ such that $ℵ_{1}$ is a precalibre of $G$ (hence, $G$ has countable cellularity), all countable subsets of $G$ are closed and $C$ -embedded in $G$ , but $G$ is not $ℝ$ -factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.

A decomposition theorem for compact groups with an application to supercompactness

Wiesław Kubiś, Sławomir Turek (2011)

Open Mathematics

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.

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A Boolean view of sequential compactness

A characterization of Corson-compact spaces

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

A compact Fréchet space whose square is not Fréchet

A compact Hausdorff topology that is a T₁-complement of itself

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

A constructive proof of the Tychonoff's theorem for locales

A Corson compact L-space from a Suslin tree

A countably cellular topological group all of whose countable subsets are closed need not be $ℝ$ -factorizable

A decomposition theorem for compact groups with an application to supercompactness

A first countable supercompact Hausdorff space with a closed $G_{δ}$ 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 $K$ -compact spaces

Currently displaying 1 – 20 of 65