A Ring Version of Mazur’s Conjecture on Topology of Rational Points
نویسندگان
چکیده
Remark 1.2. Let W be an algebraic set defined over a number field. Then W = V1∪· · ·∪Vk, k ∈ N, where Vi is a variety and W̄ = V̄1 ∪ · · · ∪ V̄k, with W̄, V̄1, . . . , V̄k denoting the topological closure of W, V1, . . . , Vk, respectively. Further, if nW , n1, . . . , nk are the numbers of connected components of W̄, V̄1, . . . , V̄k, respectively and ni < ∞ for all i = 1, . . . , k, then nW ≤ n1+ · · ·+nk. Thus, without changing the scope of the conjecture we can apply Conjecture 1.1 to algebraic sets instead of varieties.
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