2024/03/06 by A. E. Lipin, Lipin, Anton E., Alexander V. Osipov +1
Mathematics · #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2403.04004
openalex publication_date 2024/03/06 · openalex created_date 2024/03/10 · openalex updated_date 2026/07/28
We prove that for every normal topological space X and any function f: X → ℝ there is a continuous function g : X → ℝ such that |f(x) - g(x)| ≤ (1)/(2) supp ∈ X infO(p) supa,b ∈ O(p) |f(a) - f(b)| for all x ∈ X. As an application of this result we prove the following statements to types of tightness in a space Qp(X, ℝ) of all quasicontinuous real-valued functions with the topology τp of pointwise convergence: the countability of tightness (fan-tightness, strong fan-tightness) at a point f of space Qp(X, ℝ) implies the countability of tightness (fan-tightness, strong fan-tightness) of space Qp(X,Y) of all quasicontinuous functions from X into any non-one-point metrizable space Y. This result is the answer to the open question in the class of metrizable spaces.