A Candidate for the Generalised Real Line
نویسنده
چکیده
Let κ be an uncountable cardinal with κ = κ. In this paper we introduce Rκ, a Cauchy-complete real closed field of cardinality 2. We will prove that Rκ shares many features with R which have a key role in real analysis and computable analysis. In particular, we will prove that the Intermediate Value Theorem holds for a non-trivial subclass of continuous functions over Rκ. We propose Rκ as a candidate for extending computable analysis to generalised Baire spaces.
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