weakly semicontinuous

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Direct method in the calculus of variations — In the calculus of variations, a topic in mathematics, the direct method is a general method for constructing a proof of the existence of a minimizer for a given functional,[1] introduced by Zaremba and David Hilbert around 1900. The method… … Wikipedia
Caristi fixed point theorem — In mathematics, the Caristi fixed point theorem (also known as the Caristi Kirk fixed point theorem) generalizes the Banach fixed point theorem for maps of a complete metric space into itself. Caristi s fixed point theorem is a variation of the… … Wikipedia
Tonelli's theorem (functional analysis) — In mathematics, Tonelli s theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on L p spaces. As such, it has major implications for functional analysis and the calculus of variations.… … Wikipedia
Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… … Wikipedia
Paracompact space — In mathematics, a paracompact space is a topological space in which every open cover admits a locally finite open refinement. Paracompact spaces are sometimes also required to be Hausdorff. Paracompact spaces were introduced by Dieudonné (1944).… … Wikipedia

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