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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 which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii spaces, for which every sheaf at a point can be amalgamated in a natural way. Let denote the space of continuous real-valued functions on with the topology of pointwise convergence. Our main result...
A function f: ℝⁿ → ℝ satisfies the condition (resp. , ) 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 . Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.
We study the relation between the Lusin-Menchoff property and the -“semiseparation” property of a fine topology in normal spaces. Three examples of normal topological spaces having the -“semiseparation” property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space.
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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