Most of the fundamental concepts of topological classification and characterization are based on an assumption of short-range coupling. These cognitions may largely fail for long-range systems with power-law decay exponent $\beta$, which have received increasing attention with the fast progress in artificial assembled quantum simulators. Especially, the bulk-boundary correspondence may weaken $(0<\beta <1)$ or completely break down $(\beta =0)$, cases where the bulk topological invariant alone is insufficient to determine the number of edge modes. Here, we propose a mapped bulk-boundary correspondence to characterize topological edge modes of nonlocal systems with strong long-range coupling $0\le \beta <1$. The analytic results show that strong long-range hoppings can induce infinitely large topological regions. Our method is also applicable to the Rydberg-dressed systems with an infinite dressing radius.

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