Hi,
I got these definitions and one example sentence from my young friend's Collins/Cobuild Compact English Learner's Dictionary and want to know the following.
1. Why the phrase "the type of surroundings" and not "the types of surroundings"?
The setting for something is the particular place or the type of surroundings in which it is located or where it happens. The thought is that if a thing is in one particular location, its surroundings are of one type.
2. Why does the sentence/phrase given as an example have an article when the word correspondence is noted as an uncountable noun?
Correspondence is the act of writing letters to someone ... a long correspondence with a close college friend. It's usually an uncountable noun, but it can also be countable, as in the latter phrase which means an exchange of letters.
Best wishes, Clive