Displaying similar documents to “The family of I -density type topologies”

Analytic functions are ℐ -density continuous

Krzysztof Ciesielski, Lee Larson (1994)

Commentationes Mathematicae Universitatis Carolinae

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A real function is ℐ -density continuous if it is continuous with the ℐ -density topology on both the domain and the range. If f is analytic, then f is ℐ -density continuous. There exists a function which is both C ∞ and convex which is not ℐ -density continuous.

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...

On topologies generated by some operators

Katarzyna Flak, Jacek Hejduk (2013)

Open Mathematics

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The paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.