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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?

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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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  • I agree. If you could make a noun from "simply connected" by adding "-ness" to it, you could get "simply connectedness". But the grammatical problem with this is that you can't add "-ness" to multi-word phrases -- you can only add "-ness" to words. That's why "simply connectedness" doesn't make it.
    – Greg Lee
    Commented Feb 2, 2015 at 15:21
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    @GregLee, anemone, I can't disagree about that part. But what if there's a hyphen in between? Can "-ness" be added to hyphenated complexes of words? I mean, will "simply-connectedness" be counted as grammatical?
    – N Unnikrishnan
    Commented Feb 3, 2015 at 7:17
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    No. Use of a hyphen is just a spelling convention. It doesn't change anything -- "simply connected" is still not a word. "A rose by any other name would smell as sweet." Anyway, I suspect that -ness can't be added to compound words, either, though I can't think relevant examples right now.
    – Greg Lee
    Commented Feb 3, 2015 at 13:00
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    @NUnnikrishnan In compound modifiers used in a noun phrase, a hyphen can be used to change the implicit dependency. Here, no hyphen is needed because "simply", as an adverb, can only depend on "connected", as an adjective. So in "simply-connected", the hyphen is superfluous; it is likewise superfluous in "simple-connectedness". I'd not dream of using "simply-connectedness", but if you do among topologists, I think you will still be comprehensible.
    – anemone
    Commented Feb 3, 2015 at 17:52
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It appears that the standard usage is "simple connectedness", although some sources include a hyphen.

  1. http://en.wikipedia.org/wiki/Connectedness#Connectivity
  2. http://www.researchgate.net/publication/231141910_Simple_connectedness_of_spacetime_in_the_path_topology
  3. https://math.stackexchange.com/questions/719450/is-there-any-point-set-definition-of-simple-connectedness
  4. http://www.math.washington.edu/~lee/Courses/441-2012/simplyconn.pdf?v2 (PDF)
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  • Oh yes, simple(-)connectedness is what we all use at present, but I thought English.SE might have a different answer. After all, wikipedia is not an authentic source on nuances of grammar. My problem with unhyphenated 'simple connectedness' is that, doesn't it mean something else? In the sense, 'simple' could be an adjective serving the whole compound 'connected space'. For, 'simple' itself serves as a mathematical adjective (in more than one context, sense, as a matter of fact). Like 'simple groups' (hence 'simple topological groups' also) etc.
    – N Unnikrishnan
    Commented Feb 2, 2015 at 7:09

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