Abstract
Abstract Let 𝐶 = 𝐶[0, 1] denote the Banach space of continuous real functions on [0, 1] with the sup norm and let 𝐶* denote the topological subspace of 𝐶 consisting of functions with values in [0, 1]. We investigate the preimages of residual sets in 𝐶 under the operation of superposition Φ : 𝐶 × 𝐶* → 𝐶, Φ(𝑓, 𝑔) = 𝑓 ○ 𝑔. Their behaviour can be different. We show examples when the preimages of residual sets are nonresidual of second category, or even nowhere dense, and examples when the preimages of nontrivial residual sets are residual.
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