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It is proven that the set of all (bounded linear) operators on a complex infinite dimensional Banach space having disconnected spectra is an open uniformly dense subset of the algebra of all operators. AM S 1970 subject classifications. Primary 47A15; Secondary 47 A10, 47A55.doi:10.1090/s0002-9904-1972-12981-1 fatcat:fmalnakkbze4pnefuphan3ygh4