Linked from
The 22 pages that link to Thermodynamic cycle, each with the reason it gives.
Thermodynamic stateBroader topic: The cycle closes because the final state equals the initial state.
State functionBroader topic: A state function has zero net change over any completed cycle.
State variableBroader topic: State variables return to their starting values after a complete cycle.
Clausius theoremBroader topic: The theorem applies to processes that close into such a cycle.