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arXiv · 2607.11932

Approximate monotonicity, subadditivity, and convexity in weighted topologies

Angshuman R. Goswami
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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.

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Angshuman R. Goswami. 2026-07-10. Approximate monotonicity, subadditivity, and convexity in weighted topologies. https://arxiv.org/abs/2607.11932

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