Metrizability of the Space of R-places of a Real Function Field

Content Provider	Semantic Scholar
Author	Marshall, M.
Copyright Year	2009
Abstract	For n = 1, the space of R-places of the rational function field R(x1, . . . , xn) is homeomorphic to the real projective line. For n ≥ 2, the structure is much more complicated. We prove that the space of R-places of the rational function field R(x, y) is not metrizable. We explain how the proof generalizes to show that the space of R-places of any finitely generated formally real field extension of R of transcendence degree ≥ 2 is not metrizable. We also consider the more general question of when the space of R-places of a finitely generated formally real field extension of a real closed field is metrizable.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://math.usask.ca/~marshall/met109.pdf
Alternate Webpage(s)	https://math.usask.ca/~marshall/met109.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article