First of all, the risk-free arbitrage interval is the interval of net profit after deducting your arbitrage cost. If your cost increases and you want to get the same arbitrage profit, then the upper and lower boundaries of your arbitrage range will also expand, otherwise your profit will shrink.

Note that the risk-free arbitrage interval is artificially calculated, not divorced from the market. In other words, after the cost increases, you still have to get the same profit, so the interval will inevitably expand after the final calculation formula (the expanded part is the part where your handling fee increases and the cost increases). This means that after the cost is expanded, there will be fewer trading opportunities that meet the interval conditions.

Supplementary answer: Your understanding is correct. If the profit is determined and the cost increases, from another perspective, your arbitrage scope is narrowed.