Displaying similar documents to “A continuum $X$ such that $C(X)$ is not continuously homogeneous”

On the hyperspace C n ( X ) / C n K ( X )

José G. Anaya, Enrique Castañeda-Alvarado, José A. Martínez-Cortez (2021)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a continuum and n a positive integer. Let C n ( X ) be the hyperspace of all nonempty closed subsets of X with at most n components, endowed with the Hausdorff metric. For K compact subset of X , define the hyperspace C n K ( X ) = { A C n ( X ) : K A } . In this paper, we consider the hyperspace C K n ( X ) = C n ( X ) / C n K ( X ) , which can be a tool to study the space C n ( X ) . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility. ...

On affinity of Peano type functions

Tomasz Słonka (2012)

Colloquium Mathematicae

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We show that if n is a positive integer and 2 , then for every positive integer m and for every real constant c > 0 there are functions f , . . . , f n + m : such that ( f , . . . , f n + m ) ( ) = n + m and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that ( f i , . . . , f i ) ( y ) = y + w for y x + ( - c , c ) × n - 1 .

Making holes in the cone, suspension and hyperspaces of some continua

José G. Anaya, Enrique Castañeda-Alvarado, Alejandro Fuentes-Montes de Oca, Fernando Orozco-Zitli (2018)

Commentationes Mathematicae Universitatis Carolinae

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A connected topological space Z is unicoherent provided that if Z = A B where A and B are closed connected subsets of Z , then A B is connected. Let Z be a unicoherent space, we say that z Z makes a hole in Z if Z - { z } is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.

Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

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For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2 X can be extended to a Whitney map for 2 X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, Jerzy Krzempek (2010)

Fundamenta Mathematicae

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For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum S n , α , β such that (a) d i m S n , α , β = n ; (b) t r D g S n , α , β = t r D g o S n , α , β = α ; (c) t r i n d S n , α , β = t r I n d S n , α , β = β ; (d) if β < ω(⁺), then S n , α , β is separable and first countable; (e) if n = 1, then S n , α , β can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then S n , α , β can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then S n , α , β can be made chainable and hereditarily indecomposable. In...

Singular arc-like continua

Tadeusz Maćkowiak

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CONTENTSIntroduction.......................................................................................................51. Preliminaries.................................................................................................6  A. Mappings....................................................................................................6  B. Arc-like continua.........................................................................................8  C. Pseudosuspensions...................................................................................8  D....

The Rothberger property on C p ( Ψ ( 𝒜 ) , 2 )

Daniel Bernal-Santos (2016)

Commentationes Mathematicae Universitatis Carolinae

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A space X is said to have the Rothberger property (or simply X is Rothberger) if for every sequence 𝒰 n : n ω of open covers of X , there exists U n 𝒰 n for each n ω such that X = n ω U n . For any n ω , necessary and sufficient conditions are obtained for C p ( Ψ ( 𝒜 ) , 2 ) n to have the Rothberger property when 𝒜 is a Mrówka mad family and, assuming CH (the Continuum Hypothesis), we prove the existence of a maximal almost disjoint family 𝒜 for which the space C p ( Ψ ( 𝒜 ) , 2 ) n is Rothberger for all n ω .

-sums and the Banach space / c

Christina Brech, Piotr Koszmider (2014)

Fundamenta Mathematicae

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This paper is concerned with the isomorphic structure of the Banach space / c and how it depends on combinatorial tools whose existence is consistent with but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that / c does not have an orthogonal -decomposition, that is, it is not of the form ( X ) for any Banach space X. The main local result is that it is consistent that ( c ( ) ) does not embed isomorphically into / c , where is the cardinality of the continuum,...

Continuous images of Lindelöf p -groups, σ -compact groups, and related results

Aleksander V. Arhangel&#039;skii (2019)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that there exists a σ -compact topological group which cannot be represented as a continuous image of a Lindelöf p -group, see Example 2.8. This result is based on an inequality for the cardinality of continuous images of Lindelöf p -groups (Theorem 2.1). A closely related result is Corollary 4.4: if a space Y is a continuous image of a Lindelöf p -group, then there exists a covering γ of Y by dyadic compacta such that | γ | 2 ω . We also show that if a homogeneous compact space Y is...

Moser's Inequality for a class of integral operators

Finbarr Holland, David Walsh (1995)

Studia Mathematica

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Let 1 < p < ∞, q = p/(p-1) and for f L p ( 0 , ) define F ( x ) = ( 1 / x ) ʃ 0 x f ( t ) d t , x > 0. Moser’s Inequality states that there is a constant C p such that s u p a 1 s u p f B p ʃ 0 e x p [ a x q | F ( x ) | q - x ] d x = C p where B p is the unit ball of L p . Moreover, the value a = 1 is sharp. We observe that F = K 1 f where the integral operator K 1 has a simple kernel K. We consider the question of for what kernels K(t,x), 0 ≤ t, x < ∞, this result can be extended, and proceed to discuss this when K is non-negative and homogeneous of degree -1. A sufficient condition on K is found for...

On two-to-one continuous functions

J. Mioduszewski

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CONTENTSIntroduction................................................................................................................................................................................3I. General properties of k-to-one functions on locally compact spaces1. Multi-valued functions Ф and ψ......................................................................................................................................... 62. The proof of (I.11)..................................................................................................................................................................

A localization property for B p q s and F p q s spaces

Hans Triebel (1994)

Studia Mathematica

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Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

C * -points vs P -points and P -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

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In a Tychonoff space X , the point p X is called a C * -point if every real-valued continuous function on C { p } can be extended continuously to p . Every point in an extremally disconnected space is a C * -point. A classic example is the space 𝐖 * = ω 1 + 1 consisting of the countable ordinals together with ω 1 . The point ω 1 is known to be a C * -point as well as a P -point. We supply a characterization of C * -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...