and topological spaces
C. Dorsett (1978)
Matematički Vesnik
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C. Dorsett (1978)
Matematički Vesnik
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D. Janković (1981)
Matematički Vesnik
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M. R. Žižović (1986)
Matematički Vesnik
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K. K. Dube (1974)
Matematički Vesnik
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R. W. Knight (2007)
Fundamenta Mathematicae
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We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points of cardinality , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.
Aleksander V. Arhangel'skii, J. van Mill (2016)
Commentationes Mathematicae Universitatis Carolinae
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It is known that every remainder of a topological group is Lindelöf or pseudocompact. Motivated by this result, we study in this paper when a topological group has a normal remainder. In a previous paper we showed that under mild conditions on , the Continuum Hypothesis implies that if the Čech-Stone remainder of is normal, then it is Lindelöf. Here we continue this line of investigation, mainly for the case of precompact groups. We show that no pseudocompact group, whose weight...
Adam Bartoš (2016)
Commentationes Mathematicae Universitatis Carolinae
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A subset of a product of topological spaces is called -thin if every its two distinct points differ in at least coordinates. We generalize a construction of Gruenhage, Natkaniec, and Piotrowski, and obtain, under CH, a countable space without isolated points such that contains an -thin dense subset, but does not contain any -thin dense subset. We also observe that part of the construction can be carried out under MA.
Ahmad Al-Omari, Takashi Noiri (2017)
Archivum Mathematicum
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A topological space is said to be -Lindelöf [1] if every cover of by cozero sets of admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of -Lindelöf spaces.
Franklin D. Tall (2002)
Fundamenta Mathematicae
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Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by . Suppose is homeomorphic to the irrationals; must ? We have partial results. We also answer a question of Gruenhage by showing that if is homeomorphic to the “Long Cantor Set”, then .
Taras Banakh, Artur Bartoszewicz, Szymon Głąb, Emilia Szymonik (2012)
Colloquium Mathematicae
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For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable....
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Reynaldo Rojas-Hernández (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...
Jiří Matoušek, Martin Tancer, Uli Wagner (2011)
Journal of the European Mathematical Society
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Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all...
Zhanmin Zhu (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let be two non-negative integers. A left -module is called -injective, if for every -presented left -module . A right -module is called -flat, if for every -presented left -module . A left -module is called weakly --injective, if for every -presented left -module . A right -module is called weakly -flat, if for every -presented left -module . In this paper, we give some characterizations and properties of -injective modules and -flat modules in...
Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .
Jan J. Dijkstra, Dave Visser (2010)
Fundamenta Mathematicae
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Erdős space is the “rational” Hilbert space, that is, the set of vectors in ℓ² with all coordinates rational. Erdős proved that is one-dimensional and homeomorphic to its own square × , which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of . Let , n ∈ ℕ, be the n-dimensional Menger continuum in , also known as the n-dimensional Sierpiński carpet, and let D be a countable dense subset of . We consider the topological group...