Abstract

We investigate the topological properties of scalar field configurations influenced by non-commutative geometry and time-dependent perturbations. Specifically, we analyze the connectedness of level sets of scalar fields, compute the fractal dimensions of generated patterns, and study the impact of varying non-commutative parameters. Utilizing numerical simulations, we provide evidence of topological bifurcations induced by non-commutative corrections. The analysis is framed within point set topology, and the results are formalized using the theorem-proof structure.