I have encountered a confusing sentence in a math textbook:
Suppose F is a holomorphic function in the sector S that is continuous on the closure of S.
What does that mean in the above sentence? Does it mean the function F?
can be interpreted in two ways, because that can refer to the sector or the holomorphic function in the sector. Of course, from the context we know that it really refers to the latter.
You'll have to ask the author.
Grammatically, however, that is a restrictive relative pronoun that refers to "the sector S", and the relative clause means that sector S is continuous on the closure of sector S.
Knowing nothing about math, I can't tell you what this means, but that interpretation makes no semantic sense.
Because this makes no sense to me, I'd say that that is supposed to refer to "the holomorphic function F", as it would in a properly written sentence (but still a stylistically awkward kind of "read my mind, please, because I can't be bothered to express myself clearly" sentence):
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