How to choose an article for a mathematical/physical/scientific term?

Question

I've read a lot of articles on the internet, watched youtube videos on this topic and the explanation seems to be clear. But when it comes to practice, I'm often struggling with choosing correct articles. Especially, when talking about something more or less scientific or abstract.

Say, "Euclidean Space".

1. Should it be "THE Euclidean space", because it's kind of a "family of spaces"?
2. Or "A Euclidean space", because we're talking about some particular type of space, one of many.
3. Or should it be used without any article at all, because of the "space" word it contains, which is general enough to be referred to in this way?

What rule to follow to decide which usage is correct in such cases?

Answer 1

To the extent this answer involves topology, it should be taken with a pound of salt.

In general, when some single thing is distinguished by an adjective formed from a proper noun, it does not take an article any more than a proper name takes an article.

Victorian England was one of the five Great Powers of Europe.

When a plural set of things is distinguished by an adjective formed from a proper noun, the collective usually does not take an article.

European countries are democracies.

If, however, we are referring to members of the set, we do use articles.

The European country that I most like to visit is Italy.

A European country that I have not visited is Bulgaria.

These are general rules with exceptions

The Victorian England of Arnold and Browning was not the Victorian England of Swinburne and Wilde

That sentence implies that Victorian England was not a single thing, but rather a collection of things.

My understanding (which may be wrong) is that Euclidean space is a single mathematical concept. So if we are referring to the concept, no article should be used.

Before the nineteenth century, no one studied any geometry except that of Euclidian space.

However, there many spaces that are exemplars of that concept. So if you are talking about one or more paricular exemplars of that concept, articles apply.