Why is an article for a singular countable noun sometimes omitted?
I know singular countable nouns need 'a / an / the' before them. But when exactly do you leave them? I heard in TV series. They didn't put any article for a singular countable noun.

For example:
Door is open. So I came in. Why not "The door is open"? Because the speakers know which door they're talking about. There is only one door.

Thank you in advance.

Question

Why is an article for a singular countable noun sometimes omitted?
I know singular countable nouns need 'a / an / the' before them. But when exactly do you leave them? I heard in TV series. They didn't put any article for a singular countable noun.

For example: 
Door is open. So I came in. >>> Why not "The door is open"? Because the speakers know which door they're talking about. There is only one door.

Thank you in advance.

Answer

This is very casual spoken speech.  This is not acceptable in written English.

Answer

In the example you give, it would be more correct for the person to say "The door is open"

If the speaker didn't say "the" it is technically incorrect. This is a very informal/slangy way of speaking.

Answer

Which TV Series?  Who said it?  What else is going on in the scene?

It would be very, very odd for a native speaker to leave out the article in that sentence.  In fact, leaving it out calls attention to the fact it is missing.   I think there's context missing.

Answer

We would say that is lazy speech. Basically understandable, but very poor.