Complex sentence: The complement of the closure of "D" in "S" was called the corona by, and the corona theorem states that the corona is empty, or in other words the open unit disc "D" is dense in the spectrum.
Split into simpler sentences: The complement of the closure of "D" in "S" was called the corona by. The corona theorem states that the corona is empty, or in other words the open unit disc is dense in the spectrum.