analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … … An ordered field is real closed if it satisfies the following two properties: Any non-negative element in has a square root in ; Any odd-degree polynomial function with coefficients in has a root in . Notice that the order on a real closed field is definable from the algebraic...