A class of -sets
David Grow (1987)
Colloquium Mathematicae
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David Grow (1987)
Colloquium Mathematicae
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Alejandro Illanes (2006)
Colloquium Mathematicae
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For a metric continuum X, let C(X) (resp., ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and be the induced functions given by and . In this paper, we prove that: • If is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1]...
Qing Li (2010)
Colloquium Mathematicae
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This paper is a continuation of the investigation of almost Prüfer v-multiplication domains (APVMDs) begun by Li [Algebra Colloq., to appear]. We show that an integral domain D is an APVMD if and only if D is a locally APVMD and D is well behaved. We also prove that D is an APVMD if and only if the integral closure D̅ of D is a PVMD, D ⊆ D̅ is a root extension and D is t-linked under D̅. We introduce the notion of an almost t-splitting set. denotes the ring , where S is a multiplicatively...
Ewa Strońska (2006)
Colloquium Mathematicae
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It is proved that the following conditions are equivalent: (a) f is an almost everywhere continuous function on ; (b) f = g + h, where g,h are strongly quasicontinuous on ; (c) f = c + gh, where c ∈ ℝ and g,h are strongly quasicontinuous on .
Andrea R. Nahmod, Gigliola Staffilani (2015)
Journal of the European Mathematical Society
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We also prove a long time existence result; more precisely we prove that for fixed there exists a set , such that any data , evolves up to time into a solution with , . In particular we find a nontrivial set of data which gives rise to long time solutions below the critical space , that is in the supercritical scaling regime.
Viktor Harangi (2011)
Fundamenta Mathematicae
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Let be arbitrary nonzero real numbers. An -decomposition of a function f:ℝ → ℝ is a sum where is an -periodic function. Such a decomposition is not unique because there are several solutions of the equation with -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the -decomposition is essentially unique. We characterize those periods for which essential...
Katusi Fukuyama (2001)
Colloquium Mathematicae
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By the method of Rio [10], for a locally square integrable periodic function f, we prove for almost every x and t > 0.
Jaume Llibre, Víctor F. Sirvent (2016)
Mathematica Bohemica
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Let be a connected closed manifold and a self-map on . We say that is almost quasi-unipotent if every eigenvalue of the map (the induced map on the -th homology group of ) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of as eigenvalue of all the maps with odd is equal to the sum of the multiplicities of as eigenvalue of all the maps with even. We prove that if is having finitely many periodic points all of them...
Matthew Daws (2011)
Studia Mathematica
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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say . In this paper, we investigate properties of . We present a short proof that can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...
G. A. Karagulyan (2007)
Studia Mathematica
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Let be the family of open rectangles in the plane ℝ² with a side of angle s to the x-axis. We say that a set S of directions is an R-set if there exists a function f ∈ L¹(ℝ²) such that the basis differentiates the integral of f if s ∉ S, and almost everywhere if s ∈ S. If the condition holds on a set of positive measure (instead of a.e.) we say that S is a WR-set. It is proved that S is an R-set (resp. a WR-set) if and only if it is a (resp. a ).
H. S. Mustafayev (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let A be a complex, commutative Banach algebra and let be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space is scattered (i.e., has no nonempty perfect subset). (b) Weakly almost periodic...
Chuan Jen Chyan, Andrzej Fryszkowski (2004)
Studia Mathematica
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A new approach to differentiation on a time scale is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: → ℝ has a right derivative f₊’(x) for -almost all x ∈ . Moreover, .
Nijjwal Karak (2017)
Czechoslovak Mathematical Journal
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In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point in a metric measure space is called a generalized Lebesgue point of a measurable function if the medians of over the balls converge to when converges to . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function....
David Swanson (2010)
Colloquium Mathematicae
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Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function possesses an derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space . Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.
G. Ervynck (1991)
Matematički Vesnik
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Jan Kurek, Włodzimierz M. Mikulski (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let be the category of -dimensional manifolds and local diffeomorphisms and let be the tangent functor on . Let be the category of real vector spaces and linear maps and let be the category of -dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors admitting -natural operators transforming classical linear connections on -dimensional manifolds into almost complex structures on .
Fabien Durand (2011)
Journal of the European Mathematical Society
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The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let and be two multiplicatively independent Perron numbers. Then a sequence , where is a finite alphabet, is both -substitutive and -substitutive if and only if is ultimately...
Stefan Neuwirth (1998)
Studia Mathematica
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We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between ...
Ananga Kumar Das, Pratibha Bhat, Ria Gupta (2016)
Mathematica Bohemica
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The notion of -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost -normal spaces, which is a simultaneous generalization of -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak -normality, in terms of -closed sets, which turns out to be a simultaneous generalization of -normality and -normality. A space is said to be weakly -normal (w-normal if for every...
G. Pantsulaia (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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An example of a non-zero non-atomic translation-invariant Borel measure on the Banach space is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition "-almost every element of has a property P" implies that “almost every” element of (in the sense of [4]) has the property P. It is also shown that the converse is not valid.
Raafat Abo-Zeid (2015)
Archivum Mathematicum
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In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation where are positive real numbers and the initial conditions , , , are real numbers.