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We characterize lower semi-Fredholm and Fredholm of weighted compositionoperators on $C(K)$ in the case when the corresponding map is an opensurjection of the compact space $K$ onto itself. The obtained criterionsinvolve the notion of almost homeomorphisms of compact spaces.

Spectrum of weighted composition operators. Part VIII. Lower  semi-Fredholm and Fredholm spectra of weighted compositions on $C(K)$, case  of non-invertible surjections