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 … … The intermediate value theorem (IVT) is a fundamental principle of analysis which allows one to find a desired value by interpolation. It says that a continuous function from an interval to the real numbers (all with its Euclidean topology) takes all values in between and . The...