The Lefschetz coincidence theorem in o-minimal expansions of fields
نویسندگان
چکیده
منابع مشابه
A Lefschetz-type Coincidence Theorem
A Lefschetz-type coincidence theorem for two maps f, g : X → Y from an arbitrary topological space to a manifold is given: Ifg = λfg, that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg 6= 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y ...
متن کاملStrongly minimal expansions of (C,+) definable in o-minimal fields
We characterize those functions f : C → C definable in o-minimal expansions of the reals for which the structure (C,+, f) is strongly minimal: such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy: an algebraically closed field is definable in certain strongly minimal structures which are definabl...
متن کاملAn additive measure in o-minimal expansions of fields
Given an o-minimal structure M which expands a field, we define, for each positive integer d, a real valued additive measure on a Boolean algebra of subsets of Md and we prove that all the definable sets included in the finite part Fin(Md) of Md are measurable. When the domain of M is R we obtain the Lebesgue measure, but restricted to a proper subalgebra of that of the Lebesgue measurable sets...
متن کاملSaturated O-minimal Expansions of Real Closed Fields
In [KKMZ02] the authors gave a valuation theoretic characterization for a real closed field to be κ-saturated, for a cardinal κ ≥ א0. In this paper, we generalize the result, giving necessary and sufficient conditions for certain o-minimal expansion of a real closed field to be κ-saturated.
متن کاملO-minimal residue fields of o-minimal fields
Let R be an o-minimal field with a proper convex subring V . We axiomatize the class of all structures (R, V ) such that kind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in [8] it was shown that certain first order conditions on (R, V ) are sufficient for the o-minimality of kind. Here we prove that these conditions are also ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.07.002