How are the arch, the vault and the dome all related to one another?

Vault is an architectural term for an arched form used to provide a space with a ceiling or roof. The parts of a vault exert lateral thrust that requires a counter resistance. When vaults are built underground, the ground gives all the resistance required. However, when the vault is built above ground, various replacements are employed to supply the needed resistance. An example is the thicker walls used in the case of barrel or continuous vaults. Buttresses are used to supply resistance when intersecting vaults are employed.