Function spaces over GO-spaces: Part I |
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Authors: | Raushan Z Buzyakova |
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Institution: | Mathematics Department, UNCG, Greensboro, NC 27402, USA |
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Abstract: | We describe the structure of spaces of continuous step functions over GO-spaces. We establish a relation between the Dedekind completion of a GO-space L and properties of the space of continuous functions from L to 2 with finitely many steps. We use the established relation to prove that a countably compact GO-space L has Lindelöf Cp(L) iff the Dedekind remainder of L is Lindelöf and every compact subspace of L is metrizable. Or equivalently, a countably compact GO-space L has Lindelöf Cp(L) iff every compact subspace of L is metrizable and a Gδ-set in L. Other results are obtained. |
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Keywords: | 54F05 54C35 54F65 54D20 |
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