Learn Danish: Vagten sov mens bagdøren stod åben. - The guard was sleeping while the back door stood open.

Danish doesn't have a direct equivalent to the English continuous forms like 'was doing' or 'is doing'. You simply use the past tense sov to mean either 'slept' or 'was sleeping'.

Where is the past perfect blive-passive in this sentence?

There isn't one, which is an important contrast! stod åben describes a state (the door just stood there, open). If you wanted to focus on the action of someone opening the door before the guard fell asleep, you would use the past perfect passive: var blevet åbnet (had been opened).

Why is the adjective åben not spelled åbent?

åben describes the noun bagdøren. Since bagdør is a common gender noun (an en word), the adjective takes the basic form. If the guard had left a window (et vindue) open, it would be vinduet stod åbent.

What kind of clause does mens introduce?

mens (while) introduces a subordinate clause. Here, the word order looks just like a main clause, but if we added an adverb like ikke (not), it would have to go before the verb because it is a subordinate clause: mens bagdøren ikke stod åben.