How Does the Mempool Relate to a Double-Spend Attempt?

The mempool (memory pool) is a waiting area for unconfirmed transactions. A double-spend attempt involves broadcasting two conflicting transactions that spend the same funds to the mempool.

Miners or validators typically accept the first valid transaction they see. A successful double-spend requires a malicious miner to include the conflicting transaction in a block before the honest network confirms the original one.