That assigns

Question

A vector field is a map that assigns a vector to every point in space.

I saw the above definition in one of the videos about multi variable Calculus.

Is "that" a relative pronoun modifying "a map" and thus functioning adjectivially?

Thanks

GPY · Accepted Answer

Yes, it's a relative pronoun. "that assigns a vector to every point in space" modifies "map".

BillJ · Answer

A vector field is a map_i[that _____iassigns a vector to every point in space].

You asked a similar question about "that" recently.

Traditional grammar analyses the that which is found in relative clauses as a relative pronoun. But modern grammar takes it as a clause subordinator which introduces the relative clause but is not anaphoric to some antecedent. Its function is 'marker'.

In the latter analysis, the relativised element is therefore missing in the relative clause and is represented by the "____" notation called 'gap', which here functions as subject of the relative clause and is anaphoric to "map", as I've shown.

Note that it is the entire relative clause that modifies "map", not just the relativised element.

That assigns

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