"The door is open."
Translation:문이 열려 있습니다.
있습니다 = is in the state of
문이 열려 있습니다 = The door is in the 'open' state = The door is open (where open, 열려 is an adjective)
열려(요) => 열리다 = to get opened (passive form of 열다 = to open)
문이 열려(요) = The door gets opened (opened, past participle)
바람에 의해 문이 열립니다/열려(요). The door gets opened by the wind.
They are called the "state-after" verbs. The general pattern is
"<동작동사(action verb)>아/어 있다".
• Taking your examples
열리다 - open
앉다 - sit
서다 - stand
are all action verbs
• <동작동사(action verb)>아/어 connotes a change of state, indicating that the action is complete.
열려 => reached the open state = (be) open
앉아 => reached the crouching position = (be) sitting
서 => reached the upright position = (be) standing
The action verbs are at this stage in a stative state.
• The added 있다 in the pattern stands for "stay or remain" (link-verbs). And as you correctly pointed out, it creates the continuity of this 'reached state(stative)'.
열려있다 = be (remain) open
앉아있다 = be (remain) sitting
서있다 = be (remain) standing
열리다 is a tricky verb because it can be both active(open) and passive(get opened).
문이 열립니다. The door opens. (active)
바람에 의해 문이 열립니다. The door gets opened by the wind. (passive)
In the expression "열려있다" it is the active-열리다 which is in use.
Personally, I don't think you are wrong. It's just the ambiguity created by the Eng. verb "To be".
(1) "To be" can be used both as a 'dynamic-passive' verb i.e. one used to describe a change of states from active to stative; or as a 'stative-passive' verb i.e. one describing a constant state (an adjective).
Dynamic-passives describe "change". So although they have a passive voice, they are dynamic in nature.
"get" is a better alternative for the dynamic-passive "be".
(2) In Korean, for some verbs there are different verb forms to distinguish the dynamic-passive from the stative-passive.
Many (not always) dynamic-passives are formed by means of one of the interfix -이-, -히-, -리-, -기- , inserted in the active verb form. Stative-passives are formed by means of 어/-아 있다. 있다 indicates a state that be/an existing state.
• 열다 (v) = open (dynamic active)
열리다 (v) = get opened/open
문이 열립니다 (adj) = The door gets opened or the door opens
열려 있다 = be open => stative-passive (=> predicative adjective)
문이 열려 있습니다 = The door is open (stative)
• 닫다 = shut/close (dynamic-active)
닫히다 (v) = get into the shut state = get shutted/[BritEng] shut(closed), past paticiple
문이 닫힙니다 The door gets shut(closed) / The door closes
닫혀있다 (adj) = be in the shut state = be shut, adjective
문이 닫혀 있습니다 = The door is shut(closed) (stative)
Note: Unlike "open" which can be used both as verb and adjective, adjective-"close" is not used to describe the shut-state. For such meaning, the participle "closed" is used instead.