Curvature bounds of subsets in dimension two

TL;DR

This paper demonstrates that closed subsets with no first homology in two-dimensional spaces inherit the ambient space's curvature bounds, with implications for topology.

Contribution

It establishes a link between the topology of subsets and curvature bounds in two-dimensional spaces, extending geometric understanding.

Findings

Closed subsets with vanishing first homology inherit curvature bounds

Topological properties influence geometric curvature bounds

Applications to topological classification in 2D spaces

Abstract

We show that closed subsets with vanishing first homology in two-dimensional spaces inherit the upper curvature bound from their ambient spaces and discuss topological applications.