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A well-quasi-order for continuous functions
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math.LO
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continuousfunctionsscatteredspacesmetrizableseparablewell-quasi-orderzero-dimensional
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We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achieve this, we define scattered functions, which generalize scattered spaces, and describe exhaustively scattered functions between zero-dimensional separable metrizable spaces up to continuous equivalence.
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