The space of Whitney levels is homeomorphic to
Alejandro Illanes (1993)
Colloquium Mathematicae
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Alejandro Illanes (1993)
Colloquium Mathematicae
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Ge, Ying (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Vakilabad, A.Bagheri, Vaezpour, S.Mansour (2010)
The Journal of Nonlinear Sciences and its Applications
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M. Charalambous (1996)
Fundamenta Mathematicae
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A question raised in R. G. Woods' paper has a simple solution.
Azam, Akbar, Arshad, Muhammad (2008)
The Journal of Nonlinear Sciences and its Applications
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Hans-Joachim Baues, Manfred Hartl (1996)
Fundamenta Mathematicae
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The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.
A. Ostrovsky (1995)
Fundamenta Mathematicae
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We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.
Miroslav Zelený (1996)
Fundamenta Mathematicae
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It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.
Tronin, S.N. (2002)
Sibirskij Matematicheskij Zhurnal
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Binyamin Schwarz, Uri Srebro (1996)
Banach Center Publications
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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on which are balls with respect to the complex norm in are those centered at the origin.
Katsuro Sakai, Shigenori Uehara (1999)
Fundamenta Mathematicae
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Let X = (X,d) be a metric space and let the product space X × ℝ be endowed with the metric ϱ ((x,t),(x’,t’)) = maxd(x,x’), |t - t’|. We denote by the space of bounded upper semicontinuous multi-valued functions φ : X → ℝ such that each φ(x) is a closed interval. We identify with its graph which is a closed subset of X × ℝ. The space admits the Hausdorff metric induced by ϱ. It is proved that if X = (X,d) is uniformly locally connected, non-compact and complete, then is homeomorphic...