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 ) = ∫ ∫ 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.