More reflections on compactness
Lúcia R. Junqueira, Franklin D. Tall (2003)
Fundamenta Mathematicae
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We consider the question of when , where is the elementary submodel topology on X ∩ M, especially in the case when is compact.
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Lúcia R. Junqueira, Franklin D. Tall (2003)
Fundamenta Mathematicae
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We consider the question of when , where is the elementary submodel topology on X ∩ M, especially in the case when is compact.
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.
Alan S. Dow (2015)
Commentationes Mathematicae Universitatis Carolinae
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We prove that implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality which has points . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.
A. D. Rojas-Sánchez, Angel Tamariz-Mascarúa (2016)
Commentationes Mathematicae Universitatis Carolinae
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For a topological property , we say that a space is star if for every open cover of the space there exists such that . We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf...
A. R. Olfati (2016)
Commentationes Mathematicae Universitatis Carolinae
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In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of , Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that is isomorphic to some ring of continuous functions if and only if is functionally countable. For a strongly zero-dimensional space , this is equivalent to say that is functionally countable. Hence for every -space it is equivalent to pseudo--compactness.
Wei-Feng Xuan, Wei-Xue Shi (2017)
Commentationes Mathematicae Universitatis Carolinae
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We prove that if is a first countable space with property and with a -diagonal then the cardinality of is at most . We also show that if is a first countable, DCCC, normal space then the extent of is at most .
Wei-Feng Xuan, Wei-Xue Shi (2016)
Mathematica Bohemica
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A topological space has a rank 2-diagonal if there exists a diagonal sequence on of rank , that is, there is a countable family of open covers of such that for each , . We say that a space satisfies the Discrete Countable Chain Condition (DCCC for short) if every discrete family of nonempty open subsets of is countable. We mainly prove that if is a DCCC normal space with a rank 2-diagonal, then the cardinality of is at most . Moreover, we prove that if is a first...
Taras Banakh, Robert Cauty (2001)
Fundamenta Mathematicae
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Suppose a metrizable separable space Y is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power of any subspace X ⊂ Y is not universal for the class ₂ of absolute -sets; moreover, if Y is an absolute -set, then contains no closed topological copy of the Nagata space = W(I,ℙ); if Y is an absolute -set, then contains no closed copy of the Smirnov space σ = W(I,0). On the other hand, the countable...
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.
Sergei Logunov (2022)
Commentationes Mathematicae Universitatis Carolinae
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Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
M. Kuczma
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CONTENTSPART IIntroduction............................................................................................... 31. General solution.................................................................................. 42. Preliminaries and notation................................................................ 53. solutions in *................................................ 74. Change of variables..............................................................................
A. R. Olfati (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be a zero-dimensional space and be the set of all continuous real valued functions on with countable image. In this article we denote by (resp., the set of all functions in with compact (resp., pseudocompact) support. First, we observe that (resp., ), where is the Banaschewski compactification of and is the -compactification of . This implies that for an -compact space , the intersection of all free maximal ideals in is equal to , i.e., . By applying...
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...
Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)
Annales scientifiques de l'École Normale Supérieure
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Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Dachun Yang, Sibei Yang
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Let Φ be a concave function on (0,∞) of strictly critical lower type index and (the class of local weights introduced by V. S. Rychkov). We introduce the weighted local Orlicz-Hardy space via the local grand maximal function. Let for all t ∈ (0,∞). We also introduce the BMO-type space and establish the duality between and . Characterizations of , including the atomic characterization, the local vertical and the local nontangential maximal function characterizations, are...
F. Azarpanah, M. Paimann, A. R. Salehi (2015)
Commentationes Mathematicae Universitatis Carolinae
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In this article we define the -topology on some rings of quotients of . Using this, we equip the classical ring of quotients of with the -topology and we show that with the -topology is in fact a subspace of with the -topology. Characterization of the components of rings of quotients of is given and using this, it turns out that with the -topology is connected if and only if is a pseudocompact almost -space, if and only if with -topology is connected. We also...