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Source: p 182, WordNet: An Electronic Lexical Database,
by Christiane Fellbaum PhD Linguistics (Princeton)

Graphically, mathematical lattices can be depicted as line diagrams that represent a formal concept by a small circle. [See p 181 of the link for a picture.] For each formal g,
the smallest formal concept   to whose extent g belongs   is denoted by γg, ...

Please correct me if I err, but 'to the extent of which' can be called a 'relative phrase', based on p 186, A Student's Introduction to English Grammar (2005), by Huddleston & Pullum.
My tribulations with it inspired me to Google examples 'to whose extent' for practice.

I know that as a relative determiner, whose  =  of whom  or  [of] which.
The quote concerns only objects (and not persons); so whose  =  of which. Then:
to whose extent  =  to the extent of which.

Then how do you dissect and parse this relative phrase?

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For each formal g, the smallest formal concept    to whose extent g belongs
is denoted by γg

Much more often, I hear/read "X belongs to Y", but in this sentence, to appears before belongs. Also, whose is kind of functioning here as a "possessive that" for lack of a better term.

So this sentence can be rewritten like this:

For each formal g, the smallest formal concept    that its extent g belongs to
is denoted by yg.

So:

  • Each "formal g" is associated with an "extent g" (implied).

  • Extents belong to one or more "formal concepts."

  • The smallest of these "formal concepts" is called yg.

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    @LawArea Please stop vandalizing answers by inserting spaces and newlines randomly. – snailplane May 13 '15 at 1:16
  • @snailboat My edits are not intended to be random; I am just trying to accentuate the differences. They certainly are not vandalizing answers. – NNOX Apps May 13 '15 at 1:43
  • @LawArea It's vandalism. It's not intended as vandalism, and I understand that. You're trying to contribute to the site. But that doesn't mean that making an answer harder to read with this kind of formatting is okay. – snailplane May 13 '15 at 18:52
  • @snailboat Thanks for your understanding. I genuinely thought that the formatting and spacing simplified the comparison between the two. So I'll just ask the answerer whether this helps, as below. – NNOX Apps May 13 '15 at 18:56
  • @snailboat To user 'ultrasawblade': I edited your post minorly and apologise for any offense. Please feel free to refine or revert, if my formatting and spacing discommode your answer. – NNOX Apps May 13 '15 at 18:56

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