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This implies that is bounded.
This implies that is compact.
This implies that is closed.
This implies that is nondegenerate.
This implies that is nonempty.
This implies that is nonexpansive.
This implies that is closed convex for.
This implies that is closed for all.
This implies that is increasing function on.
Notice that (ii) implies that is increasing.
This implies that is nonexpansive on.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com