Thus, there are no codepoints assigned to the range D800 to DFFF in UTF-16.

Does that mean there are no codepoints assigned to the range D800 to DFFF in 
UTF-8 and UTF-32? I assume that's the case, but just want to check to be sure.
Code points are assigned in the Unicode code point space, not in the encodings.
What Martinho writes is correct. To add some complementary information:

It depends on what you (Roger) originally meant by "assigned". According to Table 2-3 (p. 23) of the Standard, they are "assigned" in official Unicode lingo. They are not "assigned to abstract character"; in the last column the table clarifies that "assigned" (in the most general sense) is to be understood as "designated" (with the opposite "undesignated" meaning {"being up for acquiring a semantics in a future version" or equivalently "not assigned but assignable to an abstract character in the future"}). The more important thing is that they're exactly the code points ("code point" can be understood as "element of the set of contiguous integers ('codespace') containing the domain of the UTF functions, which map a code point (sequence) to [a] code unit (sequence)") which are /unmappable to a UTF/. (Martinho correctly points out that some UTFs can in principle map them, though they don't and shouldn't.)

Stephan

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