One generalization of the dynamic programming problem

Milan Vlach; Karel Zimmermann

Displaying similar documents to “One generalization of the dynamic programming problem”

Further new generalized topologies via mixed constructions due to Császár

Erdal Ekici (2015)

Mathematica Bohemica

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The theory of generalized topologies was introduced by Á. Császár (2002). In the literature, some authors have introduced and studied generalized topologies and some generalized topologies via generalized topological spaces due to Á. Császár. Also, the notions of mixed constructions based on two generalized topologies were introduced and investigated by Á. Császár (2009). The main aim of this paper is to introduce and study further new generalized topologies called $μ_{12}^{C}$ via mixed constructions...

A hit-and-miss topology for $2^{X}$ , Cₙ(X) and Fₙ(X)

Benjamín Espinoza, Verónica Martínez-de-la-Vega, Jorge M. Martínez-Montejano (2009)

Colloquium Mathematicae

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A hit-and-miss topology ( $τ_{H M}$ ) is defined for the hyperspaces $2^{X}$ , Cₙ(X) and Fₙ(X) of a continuum X. We study the relationship between $τ_{H M}$ and the Vietoris topology and we find conditions on X for which these topologies are equivalent.

A compact Hausdorff topology that is a T₁-complement of itself

Dmitri Shakhmatov, Michael Tkachenko (2002)

Fundamenta Mathematicae

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Topologies τ₁ and τ₂ on a set X are called T₁-complementary if τ₁ ∩ τ₂ = X∖F: F ⊆ X is finite ∪ ∅ and τ₁∪τ₂ is a subbase for the discrete topology on X. Topological spaces $(X, τ_{X})$ and $(Y, τ_{Y})$ are called T₁-complementary provided that there exists a bijection f: X → Y such that $τ_{X}$ and $f^{- 1} (U) : U \in τ_{Y}$ are T₁-complementary topologies on X. We provide an example of a compact Hausdorff space of size $2^{}$ which is T₁-complementary to itself ( denotes the cardinality of the continuum). We prove that the existence of a compact...

Topologies on groups determined by right cancellable ultrafilters

Igor V. Protasov (2009)

Commentationes Mathematicae Universitatis Carolinae

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For every discrete group $G$ , the Stone-Čech compactification $β G$ of $G$ has a natural structure of a compact right topological semigroup. An ultrafilter $p \in G^{*}$ , where $G^{*} = β G ∖ G$ , is called right cancellable if, given any $q, r \in G^{*}$ , $q p = r p$ implies $q = r$ . For every right cancellable ultrafilter $p \in G^{*}$ , we denote by $G (p)$ the group $G$ endowed with the strongest left invariant topology in which $p$ converges to the identity of $G$ . For any countable group $G$ and any right cancellable ultrafilters $p, q \in G^{*}$ , we show that $G (p)$ is homeomorphic to $G (q)$ if...

Generalization of the topological algebra $(C_{b} (X), β)$

Jorma Arhippainen, Jukka Kauppi (2009)

Studia Mathematica

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We study subalgebras of $C_{b} (X)$ equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.

Inverse topology in MV-algebras

Fereshteh Forouzesh, Farhad Sajadian, Mahta Bedrood (2019)

Mathematica Bohemica

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We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra $A$ and show that the set of all minimal prime ideals of $A$ , namely $Min (A)$ , with the inverse topology is a compact space, Hausdorff, $T_{0}$ -space and $T_{1}$ -space. Furthermore, we prove that the spectral topology on $Min (A)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on $Min (A)$ is finer than the inverse topology on $Min (A)$ . Finally, by open sets of the inverse topology, we define and study a congruence...

On topological groups with a small base and metrizability

Saak Gabriyelyan, Jerzy Kąkol, Arkady Leiderman (2015)

Fundamenta Mathematicae

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A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, $U_{α} : α \in ℕ^{ℕ}$ , such that $U_{α} \subset U_{β}$ whenever β ≤ α for all $α, β \in ℕ^{ℕ}$ . The class of all metrizable topological groups is a proper subclass of the class $T G_{}$ of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group $G \in T G_{}$ is metrizable, and hence G is strictly angelic. We deduce from...

The AR-Property of the spaces of closed convex sets

Katsuro Sakai, Masato Yaguchi (2006)

Colloquium Mathematicae

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Let $C o n v_{H} (X)$ , $C o n v_{A W} (X)$ and $C o n v_{W} (X)$ be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of $C o n v_{H} (X)$ and the space $C o n v_{A W} (X)$ are AR. In case X is separable, $C o n v_{W} (X)$ is locally path-connected.

Classification of spaces of continuous functions on ordinals

Leonid V. Genze, Sergei P. Gul&#039;ko, Tat'ana E. Khmyleva (2018)

Commentationes Mathematicae Universitatis Carolinae

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We conclude the classification of spaces of continuous functions on ordinals carried out by Górak [Górak R., Function spaces on ordinals, Comment. Math. Univ. Carolin. 46 (2005), no. 1, 93–103]. This gives a complete topological classification of the spaces $C_{p} ([0, α])$ of all continuous real-valued functions on compact segments of ordinals endowed with the topology of pointwise convergence. Moreover, this topological classification of the spaces $C_{p} ([0, α])$ completely coincides with their uniform classification. ...

The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology

Katsuro Sakai, Zhongqiang Yang (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let $C o n v_{F} (ℝ ⁿ)$ be the space of all non-empty closed convex sets in Euclidean space ℝ ⁿ endowed with the Fell topology. We prove that $C o n v_{F} (ℝ ⁿ) \approx ℝ ⁿ \times Q$ for every n > 1 whereas $C o n v_{F} (ℝ) \approx ℝ \times$ .