There are compound adjectives in which each word is inflected (as adjective). When they are nominalised, should each adjective be separately nominalised or only the ultimate word?
The concrete question I have in mind is the following:
In mathematics, (mathematical objects called) topological spaces are said to be 'simply connected' under certain circumstances. What should the name of the corresponding property be?
'Simple-connectedness' or 'simply connectedness'?
Should there be a hyphen in the second case? (The rules for hyphens in the adjective form are clear.)
Which is the grammatically correct usage?
Answer
In "simply connected", the word "simply" is not an inflected adjective, but an adverb modifying an adjective. In "simple connectedness", the word "simple" is an adjective modifying a noun. No hyphen is needed.
"Simply connectedness" is, therefore, ungrammatical.
The word "simple" serves as a modifier for myriad different mathematical concepts.
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