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The Cageworld series is a science fiction series by Colin Kapp which takes place in a distant future where humanity lives on nested Dyson spheres. The four books are Search for the Sun (1982) (also published as Cageworld); The Lost Worlds of Cronus (1982); The Tyrant of Hades (1984) and Star Search (1984).
Cageworld #1, Search For The Sun