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A half open door is always the same as a half closed door. And of course it is not a door when it is a jar.

What could be the answer?

Hint: We're not talking about clopen doors. All our buildings are very simply connected.

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Is it

a two-way door / revolving door at the entrances of shopping complexes /malls

Which

is semi-closed at one end means semi-open at the other and similarly quarter-open at one side means quarter-closed at the other

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    $\begingroup$ If it is a quarter closed at one end, it will be a quarter closed (three quarters open) at the other end, due to the symmetry. $\endgroup$ – boboquack Dec 8 '17 at 7:44

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