A concept of ``topological'' atom--atom neighborhood relation in a strongly fluctuating solid is introduced. The divergence of metrical and topological definitions of a cluster of atoms for a sufficiently high level of atom's displacement \xi > \xi _tr, and its consequences for an analysis of local structure in locally solid-like ordered liquids are discussed. The threshold amplitude \xi _tr is calculated for a two-dimensional (2D) close-packed lattice. The Monte Carlo simulations of a 2D system of Lennard--Jones atoms lead to a hypothesis, closely related to Lindemann's melting criterion: melting occurs for \xi = \xi _m \simeq \xi _tr, i.e. when metrical and topological approaches diverge.

PACS numbers: 64.70.Dv, 61.20.Ja