💡 Detailed Explanation
The patterns '〜まま' (mama - in the state of) and '〜っぱなし' (ppanashi - left on/kept doing) represent persistence of states, with 'っぱなし' carrying a critical nuance of negligence. They attach to past tense 'た' verbs (for まま) or the 'ます' stem of verbs (for っぱなし). Use 'っぱなし' when criticizing someone for leaving a machine running or forgetting to clean up. In this sentence, it translates perfectly as: "The door is left open.". The correct option '開け' dynamically matches the structural requirements and logical flow of the statement. The other options do not satisfy the grammatical construction or fail to convey the appropriate semantic nuance.