Metrizability of Spaces of R-places of Function Fields of Transcendence Degree 1 over Real Closed Fields
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چکیده
In this paper we discuss the question ”When do different orderings of the rational function field R(X) (where R is a real closed field) induce the same R-place?”. We use this to show that if R contains a dense real closed subfield R′, then the spaces of R-places of R(X) and R′(X) are homeomorphic. For the function field K = R(X) we prove that its space M(K) of R-places is metrizible if and only if R contains a countable dense subfield. Moreover, we show that this condition is neccessary for the metrizability of M(F ) for any function field F of transcendence degree 1 over R.
منابع مشابه
Metrizability of the Space of R-places of a Real Function Field
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