ΧΩΡΟΣ is a very broad term. A page I did way back in 2002 to help my Greek students with translation into English (hope this is helpful):
ΧΩΡΟΣ: SPACE, PLACE, AREA etc
This useful Greek word has no single English equivalent. Stavropoulos (Oxford Greek - English learner's dictionary) gives a good outline of the senses and equivalents: space, room, area, place, ground, precincts, in the more physical sense, and domain in the metaphorical sense of αρμοδιότητα, although it is not easy to see why στο χώρο της οικονομίας ("in the area of finance") should come under the first section and στο χώρο της ιατρικής ("in the domain of medicine") under the second. Note also that field would appear to be a possible translation of χώρος in both of these examples, although it is not given as an equivalent.
We may distinguish between, at one end of the scale, a "literal" sense of physical area or place, and at the other, a metaphorical sense of field or area of activity. Consider the phrases ωράριο λειτουργίας των αρχαιολογικών χώρων and Υπάρχουν προβλήματα στον αγροτικό χώρο . The first refers to pieces of land with clear boundaries - archaeological sites -, while the second does not refer to the land itself, but to the sector of the economy - the area of agriculture. In this second sense, an English translation or an English equivalent text might well have no word at all corresponding to χώρος: cf στο χώρο των ΜΜΕ in/among the media. In going from Greek to English, one tactic a translator should consider with this word is to leave it out. Conversely, in going from English to Greek, one might be inclined to insert the word.
There are two common structures in Greek: (i) to follow χώρος with a noun in the genitive indicating the activity which takes place there:
χώρος φόρτωσης loading point (e.g. for cars onto a ferry), luggage space (e.g. at the back of an estate car);
χώρος άθλησης sports facility; sports ground;
χώρος εργασίας (and εργασιακός χώρος) workplace;
χώρος άσκησης practice ground, training ground;
χώροι υποδοχής reception centres (e.g. for refugees)
χώρος οχημάτων vehicle deck, car deck (on ferry).
(ii) to precede χώρος with an adjective:
αρχαιολογικοί χώροι archaeological sites;
βοηθητικοί χώροι storage space, utility room(s) (e.g. in a house or flat, the garage, scullery, cellar, outhouses, airing cupboards, the πατάρι - a cupboard-like space over the bathroom - , αποθήκη etc);
κλειστός χώρος enclosed space, indoor;
ενοικιαζόμενοι χώροι rented premises.
English has to use more specific terms in both sets of expressions; these terms include not only the words given in Stavropoulos, but a wider set, which it is not possible to predict or invent - one just has to know them, or research them.
Examples where omission is possible or arguably desirable in English (taken from the transcripts of Greek government press briefings or other Greek texts - translations are mine - PK):
επαναφορά της ηρεμίας στον χώρο των σχολείων the return of calm to the schools
δεν υπήρξε πάντα στον χώρο της Αντιπολίτευσης η απαραίτητη ψυχραιμία the Opposition did not always show the necessary calm.
επιχειρηματία του χώρου του λιανεμπορίου retailer
το ρόλο που η Ελλάδα μπορεί να παίξει στον χώρο των Βαλκανίων the role Greece can play in the Balkans - notice the difference here (difficult to capture in English) between χώρο and περιοχή. The latter would refer to the geographical area of the Balkans; the former is more abstract and sees the Balkans not so much as a geographical entity as a field of action. In English, area covers both senses, but in this context would be taken as having primarily geographical reference.
An example where omission seems obligatory in English:
στελέχη ανήκοντα στον κυβερνητικό χώρο government officials (you cannot say officials from the area of the government; at the most you might say officials from the government side, with side contrasting government and opposition)
Now try to find English equivalents for these expressions:
1. συγκεντρωσείς που γίνονται σε δημόσιους χώρους
2. ... η Ελλάδα να ενισχύσει τη θέση της στον διεθνή χώρο
3. παραβιάσεις του ελληνικού εναέριου και θαλάσσιου χώρου
4. Δεν νομίζω ότι είναι ο κατάλληλος χώρος εδώ, για να τα συζητούμε
5. ... σε έναν τόσο ευαίσθητο χώρο, όπως είναι ο χώρος της εκπαίδευσης
6. τα προβλήματα που υπάρχουν στο χώρο της υγείας
