Many people keep their emergency funds combined with general savings. This can be a mistake if you don't have a lot of self-control. For example, not having enough money in a bank account, when you want to buy new clothes is not an emergency. You can only access cash in the emergency fund when there is an actual emergency. The problem is that everyone has a different definition of what constitutes an emergency.
Most experts agree that an emergency fund is for things you can't anticipate in advance. These emergencies include loss of work, or for dire situations essential for survival.
If you can't trust yourself to keep an independent emergency fund until you need it, then just open a separate savings account at a different institution than the one you use for routine savings. Having your funds at another bank creates an additional barrier between you and the money, which means it tends to put a limit on not spending that emergency fund.