To solve this question, the user needs to know about the concept of tablespaces and recovery methods in Oracle database.

Closed recovery is a type of database recovery method in which all the data files of the database are restored from a backup and then the redo logs are applied to bring the database to a consistent state. Closed recovery is required when the database is in a state of complete failure and no data is available in the memory structures.

Only those tablespaces whose data files are so critical that they cannot be recovered using an open recovery method require a closed recovery.

Now, let's go through each option and identify if it requires a closed recovery or not:

A. USERS: This tablespace contains the user's data. It does not require a closed recovery if it gets damaged because it can be restored using an open recovery method.

B. TOOLS: This tablespace contains the database tools data. It does not require a closed recovery if it gets damaged because it can be restored using an open recovery method.

C. UNDO: This tablespace contains the undo data. It does not require a closed recovery if it gets damaged because it can be restored using an open recovery method.

D. INDEX: This tablespace contains the database index data. It does not require a closed recovery if it gets damaged because it can be restored using an open recovery method.

E. SYSTEM: This tablespace contains the system data. It is critical to the functioning of the database. If its data files are damaged, a closed recovery is required to restore it from a backup.

Therefore, the correct answer is:

The Answer is: E (SYSTEM)