-directed inverse systems of continuous images of arcs.
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Lončar, Ivan (2000)
International Journal of Mathematics and Mathematical Sciences
Mihail G. Tkachenko (1991)
Commentationes Mathematicae Universitatis Carolinae
For every topological property , we define the class of -approximable spaces which consists of spaces X having a countable closed cover such that the “section” has the property for each . It is shown that every -approximable compact space has , if is one of the following properties: countable tightness, -scatteredness with respect to character, -closedness, sequentiality (the last holds under MA or ). Metrizable-approximable spaces are studied: every compact space in this class has...
David Booth (1974)
Fundamenta Mathematicae
Ingo Bandlow (1991)
Commentationes Mathematicae Universitatis Carolinae
We characterize Corson-compact spaces by means of countable elementary substructures.
Friedrich W. Bauer (1977)
Journal für die reine und angewandte Mathematik
Misra, Prabduh Ram, Vinodkumar (1981)
International Journal of Mathematics and Mathematical Sciences
Ondrej Kalenda (2000)
Collectanea Mathematica
A. Błaszczyk, U. Lorek (1978)
Colloquium Mathematicae
S. A. Argyros, P. Dodos, V. Kanellopoulos (2008)
Murray G. Bell (1996)
Commentationes Mathematicae Universitatis Carolinae
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 .
Petr Simon (1980)
Commentationes Mathematicae Universitatis Carolinae
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 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...
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 -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...
Igor Kříž (1985)
Commentationes Mathematicae Universitatis Carolinae
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.
Mihail G. Tkachenko (2023)
Commentationes Mathematicae Universitatis Carolinae
We construct a Hausdorff topological group such that is a precalibre of (hence, has countable cellularity), all countable subsets of are closed and -embedded in , but is not -factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.
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.
Murray G. Bell (1980)
Colloquium Mathematicae
Karl Hofmann (1970)
Fundamenta Mathematicae
A. J. Ward (1975)
Czechoslovak Mathematical Journal
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