Displaying similar documents to “Closed mappings are open at a G δ set”

Mapping hierarchy for dendrites

J. J. Charatonik, W. J. Charatonik, J. R. Prajs

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AbstractLet a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we define Y ≤ F X if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order ≤ F in the family of dendrites, where F is one of the following classes of mappings: retractions, monotone, open, confluent or weakly confluent mappings. In particular, we investigate minimal and maximal elements, chains and antichains in the quasi-order ≤ F , and characterize spaces...

The Brouwer Fixed Point Theorem for Some Set Mappings

Dariusz Miklaszewski (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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For some classes X ⊂ 2 ₙ of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.

Łojasiewicz Exponent of Overdetermined Mappings

Stanisław Spodzieja, Anna Szlachcińska (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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A mapping F : ℝ ⁿ → ℝ m is called overdetermined if m > n. We prove that the calculations of both the local and global Łojasiewicz exponent of a real overdetermined polynomial mapping F : ℝ ⁿ → ℝ m can be reduced to the case m = n.

Čech-Stone-like compactifications for general topological spaces

Miroslav Hušek (1992)

Commentationes Mathematicae Universitatis Carolinae

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The problem whether every topological space X has a compactification Y such that every continuous mapping f from X into a compact space Z has a continuous extension from Y into Z is answered in the negative. For some spaces X such compactifications exist.

Weak-bases and D -spaces

Dennis K. Burke (2007)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that certain weak-base structures on a topological space give a D -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Hence, quotient mappings, with compact fibers, from metric spaces have a D -space image. What about quotient s -mappings? Arhangel’skii and Buzyakova have shown that spaces with a point-countable base...

Bond ionization energies: thiophosphoryl compounds

Marco V. Andreocci, Carla Cauletti, Claudio Furlani (1977)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Negli spettri fotoelettronici (p.e.) indotti da radiazione ultra-violetta di serie omologhe di composti, si trovano bande in ben definite regioni di energia, che possono essere assegnate empiricamente a ionizzazione di legami specifici o di coppie solitarie di elettroni. L’effetto dell'intorno chimico sulle energie di ionizzazione si esplica in piccoli spostamenti, che hanno una dipendenza approssimativamente lineare dall'ettronegatività di atomi o gruppi vicini. La discussione riguarda...

Strong Cohomological Dimension

Jerzy Dydak, Akira Koyama (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that I n d G X = d i m G X if X is a separable metric ANR and G is a countable Abelian group. Hence d i m ℤ X = d i m X for any separable metric ANR X.