[Frontiers in Mathematics] Hölder and locally Hölder Continuous Functions, and Open Sets of Class C^k, C^{k,lambda} || Hölder and locally Hölder continuous functions. The linear spaces $$C^{k}(\Omega), C^{k,\lambda}(\Omega),\; \mathrm{and}\;C^{k,\lambda}_{\mathrm {loc}}(\Omega)$$

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