Let’s say I have a mathematical property such as (the?) connectedness of a topological space. Do I need to use the definitive article if I refer to it?

For example:

(The?) connectedness of space S does not guarantee (the?) path-connectedness of S.

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  • I don't know any official rule about this (which is why this is a comment and not an answer), but my intuition, as a mathematician, is that your example with "the connectedness of space S" indicates that S is in fact connected. Without "the", it's more likely to be hypothetical, i.e., even if S were connected, it might not be path-connected. – Andreas Blass Dec 23 '18 at 1:53

Articles are often omitted in mathematical writing and discourse, for the sake of brevity. The rules, however, are quite complex, and are usually learned by practise and example. See Writing Mathematical Papers in English by Dr. Jerzy Trzeciak for more information.

In your example, the articles can be omitted without any loss of meaning, although I make this statement from memory. I stopped doing maths decades ago.

Jerzy Trzeciak, Writing Mathematical Papers in English, European Mathematical Society, 1995

Trzeciak's text mentions article omission...

..."[i]n front of nouns referring to properties if you mention no particular object"

  • the articles can be omitted without any loss of meaning – That’s not really a good argument for what should or is allowed to be omitted in a language though. Languages thrive on redundancy and most articles, vowels, punctuation, and so on can be omitted without losing anything – it just makes texts harder to read. – Wrzlprmft Nov 24 '17 at 6:37
  • @Wrzlprmft It's just a convention that mathematicians routinely employ. I'm sure they don't do it in everyday speech and writing. – Mick Nov 24 '17 at 6:42

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