ON THE HEWITT–STROMBERG DIMENSION OF THE GRAPHS OF SUMS AND PRODUCTS OF CONTINUOUS FUNCTIONS
Rim Achour, Zhiming Li, Bilel Selmi, TINGTING WANG
Abstract
In this paper, for a typical function [Formula: see text] defined in an uncountable compact metric space [Formula: see text], we give the lower Hewitt–Stromberg dimension of graphs [Formula: see text] of the function [Formula: see text]. Moreover, we investigate the decomposition of functions within [Formula: see text] based on the lower box dimension and the lower Hewitt–Stromberg dimension, revealing significant disparities compared to the context of the packing dimension. Second, we present some results on the lower Hewitt–Stromberg dimension of graphs of sums and products of continuous functions. The main proof is that for a given real number [Formula: see text], some real-valued continuous functions in [Formula: see text] can be decomposed into the sum and product of two continuous real-valued functions, and the lower Hewitt–Stromberg dimension of the graph for each function is [Formula: see text].