In offline e-cash, you still need an online mint to initially create and validate tokens. The mint provides the cryptographic signatures that make the tokens valid. When you go offline, you carry pre-signed tokens of various denominations. These tokens can be exchanged directly without real-time verification from the mint, but the mint must have originally signed and authorized those specific tokens. So "offline" really means peer-to-peer exchange using pre-validated tokens, but the initial token creation and validation still requires an online mint.