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We provide a complete description of the spectrum and the essential spectraof weighted composition operators $T=wT_\varphi$ on $C(K)$ in the case when themap $\varphi$ is a non-invertible homeomorphism of $K$ into itself.

Spectrum of Weighted Composition Operators Part VII Essential spectra of  weighted composition operators on $C(K)$. The case of non-invertible  homeomorphisms