On weakly Gibson $F_{σ}$-measurable mappings

Olena Karlova; Volodymyr Mykhaylyuk

Displaying similar documents to “On weakly Gibson $F_{σ}$ -measurable mappings”

Domination numbers in graphs with removed edge or set of edges

Magdalena Lemańska (2005)

Discussiones Mathematicae Graph Theory

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It is known that the removal of an edge from a graph G cannot decrease a domination number γ(G) and can increase it by at most one. Thus we can write that γ(G) ≤ γ(G-e) ≤ γ(G)+1 when an arbitrary edge e is removed. Here we present similar inequalities for the weakly connected domination number $γ_{w}$ and the connected domination number $γ_{c}$ , i.e., we show that $γ_{w} (G) \leq γ_{w} (G - e) \leq γ_{w} (G) + 1$ and $γ_{c} (G) \leq γ_{c} (G - e) \leq γ_{c} (G) + 2$ if G and G-e are connected. Additionally we show that $γ_{w} (G) \leq γ_{w} (G - E ₚ) \leq γ_{w} (G) + p - 1$ and $γ_{c} (G) \leq γ_{c} (G - E ₚ) \leq γ_{c} (G) + 2 p - 2$ if G and G - Eₚ are connected and Eₚ = E(Hₚ) where Hₚ of order...

Connected components of sets of finite perimeter and applications to image processing

Luigi Ambrosio, Vicent Caselles, Simon Masnou, Jean-Michel Morel (2001)

Journal of the European Mathematical Society

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This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in $ℝ^{N}$ , introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called $M$ -connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set...

On D-connected sets in the space $V^{q}$

S. Topa (1976)

Annales Polonici Mathematici

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Weak precompactness and property (V*) in spaces of compact operators

Ioana Ghenciu (2015)

Colloquium Mathematicae

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We give sufficient conditions for subsets of compact operators to be weakly precompact. Let $L_{w *} (E *, F)$ (resp. $K_{w *} (E *, F)$ ) denote the set of all w* - w continuous (resp. w* - w continuous compact) operators from E* to F. We prove that if H is a subset of $K_{w *} (E *, F)$ such that H(x*) is relatively weakly compact for each x* ∈ E* and H*(y*) is weakly precompact for each y* ∈ F*, then H is weakly precompact. We also prove the following results: If E has property (wV*) and F has property (V*), then $K_{w *} (E *, F)$ has property (wV*). Suppose...

Weakly null sequences with upper estimates

Daniel Freeman (2008)

Studia Mathematica

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We prove that if $(v_{i})$ is a seminormalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_{i})$ , then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by $(v_{i})$ . This extends a result of Knaust and Odell, who proved this for the cases in which $(v_{i})$ is the standard basis for $ℓ_{p}$ or c₀.

On the connectivity of finite subset spaces

Jacob Mostovoy, Rustam Sadykov (2012)

Fundamenta Mathematicae

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We prove that the space $e x p_{k} ⋁ S^{m + 1}$ of nonempty subsets of cardinality at most k in a bouquet of m+1-dimensional spheres is (m+k-2)-connected. This, as shown by Tuffley, implies that the space $e x p_{k} X$ is (m+k-2)-connected for any m-connected cell complex X.

Does the endomorphism poset $P^{P}$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978

Jonathan David Farley (2023)

Mathematica Bohemica

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Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that $P$ is connected and $P^{P} ≅ Q^{Q}$ imply that $Q$ is connected”, where $P$ and $Q$ are finite nonempty posets. We show that, indeed, under these hypotheses $Q$ is connected and $P ≅ Q$ .

Proper connection number of bipartite graphs

Jun Yue, Meiqin Wei, Yan Zhao (2018)

Czechoslovak Mathematical Journal

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An edge-colored graph $G$ is proper connected if every pair of vertices is connected by a proper path. The proper connection number of a connected graph $G$ , denoted by $pc (G)$ , is the smallest number of colors that are needed to color the edges of $G$ in order to make it proper connected. In this paper, we obtain the sharp upper bound for $pc (G)$ of a general bipartite graph $G$ and a series of extremal graphs. Additionally, we give a proper $2$ -coloring for a connected bipartite graph $G$ having $δ (G) \geq 2$ and a dominating...

Characterizing matrices with $𝐗$ -simple image eigenspace in max-min semiring

Ján Plavka, Sergeĭ Sergeev (2016)

Kybernetika

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A matrix $A$ is said to have $𝐗$ -simple image eigenspace if any eigenvector $x$ belonging to the interval $𝐗 = {x : \underset{̲}{x} \leq x \leq \bar{x}}$ is the unique solution of the system $A \otimes y = x$ in $𝐗$ . The main result of this paper is a combinatorial characterization of such matrices in the linear algebra over max-min (fuzzy) semiring. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability)...

Sharkovskiĭ's theorem holds for some discontinuous functions

Piotr Szuca (2003)

Fundamenta Mathematicae

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We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected $G_{δ}$ graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_{δ}$ graph.

Property $(𝐰𝐋)$ and the reciprocal Dunford-Pettis property in projective tensor products

Ioana Ghenciu (2015)

Commentationes Mathematicae Universitatis Carolinae

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A Banach space $X$ has the reciprocal Dunford-Pettis property ( $R D P P$ ) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $R D P P$ (resp. property $(w L)$ ) if every $L$ -subset of $X^{*}$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes_{π} Y$ has property $(w L)$ when $X$ has the $R D P P$ , $Y$ has property $(w L)$ , and $L (X, Y^{*}) = K (X, Y^{*})$ .

$L$ -limited-like properties on Banach spaces

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the $p$ - $L$ -limited $^{*}$ and the $p$ -(SR $^{*}$ ) properties and characterize these classes of Banach spaces in terms of $p$ - $L$ -limited $^{*}$ and $p$ -Right $^{*}$ subsets. The $p$ - $L$ -limited $^{*}$ property is studied in some spaces of operators.

A note on weakly-supplemented subgroups of finite groups

Hong Pan (2018)

Czechoslovak Mathematical Journal

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A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G = H K$ . In the paper, we extend one main result of Kong and Liu (2014).

On families of weakly dependent random variables

Tomasz Łuczak (2011)

Banach Center Publications

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Let $ₙ^{(k)}$ be a family of random independent k-element subsets of [n] = 1,2,...,n and let $(ₙ^{(k)}, ℓ) = ₙ^{(k)} (ℓ)$ denote a family of ℓ-element subsets of [n] such that the event that S belongs to $ₙ^{(k)} (ℓ)$ depends only on the edges of $ₙ^{(k)}$ contained in S. Then, the edges of $ₙ^{(k)} (ℓ)$ are ’weakly dependent’, say, the events that two given subsets S and T are in $ₙ^{(k)} (ℓ)$ are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We...

On Hattori spaces

A. Bouziad, E. Sukhacheva (2017)

Commentationes Mathematicae Universitatis Carolinae

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For a subset $A$ of the real line $ℝ$ , Hattori space $H (A)$ is a topological space whose underlying point set is the reals $ℝ$ and whose topology is defined as follows: points from $A$ are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on $A$ which are sufficient and necessary for $H (A)$ to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...

A note on weakly-supplemented subgroups and the solvability of finite groups

Xin Liang, Baiyan Xu (2022)

Czechoslovak Mathematical Journal

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Suppose that $G$ is a finite group and $H$ is a subgroup of $G$ . The subgroup $H$ is said to be weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G = H K$ . In this note, by using the weakly-supplemented subgroups, we point out several mistakes in the proof of Theorem 1.2 of Q. Zhou (2019) and give a counterexample.

Displaying similar documents to “On weakly Gibson F σ -measurable mappings”

Displaying similar documents to “On weakly Gibson $F_{σ}$ -measurable mappings”