3-dimensional AR's which do not contain 2-dimensional ANR's
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S. Singh (1976)
Fundamenta Mathematicae
Sukhjit Singh (1974)
Fundamenta Mathematicae
Fred Galvin, Petr Simon (2007)
Fundamenta Mathematicae
A nontrivial surjective Čech closure function is constructed in ZFC.
Piotr Koszmider (2012)
Studia Mathematica
We construct a totally disconnected compact Hausdorff space K₊ which has clopen subsets K₊” ⊆ K₊’ ⊆ K₊ such that K₊” is homeomorphic to K₊ and hence C(K₊”) is isometric as a Banach space to C(K₊) but C(K₊’) is not isomorphic to C(K₊). This gives two nonisomorphic Banach spaces (necessarily nonseparable) of the form C(K) which are isomorphic to complemented subspaces of each other (even in the above strong isometric sense), providing a solution to the Schroeder-Bernstein problem for Banach spaces...
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...
Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen mapping....
Katsuya Eda, Umed H. Karimov, Dušan Repovš (2007)
Fundamenta Mathematicae
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
Aleksander Błaszczyk (1983)
Commentationes Mathematicae Universitatis Carolinae
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.
Jerry E. Vaughan (1995)
Commentationes Mathematicae Universitatis Carolinae
We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.
Alikhani-Koopaei, Aliasghar (1998)
International Journal of Mathematics and Mathematical Sciences
H. Patkowska (1978)
Fundamenta Mathematicae
J. H. V. Hunt (1971)
Colloquium Mathematicae
F. Richman (1990)
Matematički Vesnik
Jan Dijkstra (1996)
Fundamenta Mathematicae
We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.
Jiří Jelínek (2003)
Acta Universitatis Carolinae. Mathematica et Physica
Klaas Pieter Hart, Heikki J. K. Junnila, Jan van Mill (1985)
Commentationes Mathematicae Universitatis Carolinae
A. Błaszczyk (1973)
Colloquium Mathematicae
Murray G. Bell (1980)
Colloquium Mathematicae
Juan Martínez (1999)
Fundamenta Mathematicae
It was proved by Juhász and Weiss that for every ordinal α with there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that and α is an ordinal such that , then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all , we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic...
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