Approximate monotonicity, subadditivity, and convexity in weighted topologies

Angshuman R. Goswami

Approximate monotonicity, subadditivity, and convexity in weighted topologies

General Mathematics 2026-07-10 v1

Authors: Angshuman R. Goswami

Abstract

The central question of this paper is the following: "If a topological space equipped with a weight function satisfies a certain property only approximately, can we recover the original structure without significantly altering the weights?'' To each open set of a topological space, we assign a non-negative weight and study approximate versions of three natural properties: monotonicity, subadditivity, and convexity. Through this study, we develop Hyers--Ulam-type stability results in general topology. In addition, we investigate several topology-specific cases, as well as present minorant and sandwich-type results.

Keywords

approximate monotonicity subadditivity convexity weighted topology Hyers-Ulam stability minorant

Cite

@article{arxiv.2607.11932,
  title  = {Approximate monotonicity, subadditivity, and convexity in weighted topologies},
  author = {Angshuman R. Goswami},
  journal= {arXiv preprint arXiv:2607.11932},
  year   = {2026}
}