Analytic functions are $\mathcal {I}$-density continuous

Krzysztof Ciesielski; Lee Larson

Displaying similar documents to “Analytic functions are $ℐ$ -density continuous”

The family of $I$ -density type topologies

Grazyna Horbaczewska (2005)

Commentationes Mathematicae Universitatis Carolinae

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We investigate a family of topologies introduced similarly as the $I$ -density topology. In particular, we compare these topologies with respect to inclusion and we look for conditions under which these topologies are identical.

Category theorems concerning Z-density continuous functions

K. Ciesielski, L. Larson (1991)

Fundamenta Mathematicae

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The ℑ-density topology $T_{ℑ}$ on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-densitytopology is used on the domain and the range. It is shown that the family $C_{ℑ}$ of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= f: [0,1]→ℝ: f is continuous...

Mean value densities for temperatures

N. Suzuki, N. A. Watson (2003)

Colloquium Mathematicae

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A positive measurable function K on a domain D in $ℝ^{n + 1}$ is called a mean value density for temperatures if $u (0, 0) = \int \int_{D} K (x, t) u (x, t) d x d t$ for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.

Construction of an Uncountable Difference between Φ(B) and $Φ_{f} (B)$

Josh Campbell, David Swanson (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We construct a set B and homeomorphism f where f and $f^{- 1}$ have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.

A density estimate for the $3 x + 1$ problem

Ivan Korec (1994)

Mathematica Slovaca

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On relations between $f$ -density and $(R)$ -density

Václav Kijonka (2007)

Acta Mathematica Universitatis Ostraviensis

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In this paper it is discus a relation between $f$ -density and $(R)$ -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.

Kempisty's theorem for the integral product quasicontinuity

Zbigniew Grande (2006)

Colloquium Mathematicae

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A function f: ℝⁿ → ℝ satisfies the condition $Q_{i} (x)$ (resp. $Q_{s} (x)$ , $Q_{o} (x)$ ) at a point x if for each real r > 0 and for each set U ∋ x open in the Euclidean topology of ℝⁿ (resp. strong density topology, ordinary density topology) there is an open set I such that I ∩ U ≠ ∅ and $| (1 / μ (U \cap I)) \int_{U \cap I} f (t) d t - f (x) | < r$ . Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.

The density of states of a local almost periodic operator in $ℝ^{ν}$

Andrzej Krupa (2003)

Studia Mathematica

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We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on $H^{m} (ℝ^{ν})$ . The support of the density coincides with the spectrum of the operator in $L ² (ℝ^{ν})$ .

Displaying similar documents to “Analytic functions are ℐ -density continuous”

Displaying similar documents to “Analytic functions are $ℐ$ -density continuous”