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Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Boaz Tsaban, Lubomyr Zdomsky (2012)

Journal of the European Mathematical Society

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii α 1 spaces, for which every sheaf at a point can be amalgamated in a natural way. Let C p ( X ) denote the space of continuous real-valued functions on X with the topology of pointwise convergence. Our main result...

Kempisty's theorem for the integral product quasicontinuity

Zbigniew Grande (2006)

Colloquium Mathematicae

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 ∩ I ) ) ∫ U ∩ I f ( t ) d t - f ( x ) | < r . Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.

Normal spaces and the Lusin-Menchoff property

Pavel Pyrih (1997)

Mathematica Bohemica

We study the relation between the Lusin-Menchoff property and the F σ -“semiseparation” property of a fine topology in normal spaces. Three examples of normal topological spaces having the F σ -“semiseparation” property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space.

On ideal equal convergence

Rafał Filipów, Marcin Staniszewski (2014)

Open Mathematics

We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów...

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