Abstract
The notion of limit is central in analysis. Thus the concept of convergence is presented in a general framework and then in the classes of topological spaces and metric spaces. Compactness, connectedness, completeness are studied in detail. Baire’s Theorem is included as well as Ekeland’s Variational Principle. The contraction theorem is proved and as an application an existence result for ordinary differential equations is presented.
Mathematics is not an arid land in the scientific universe. It is
simultaneously the queen, maid and daughter of the
observational sciences.
La mathématique ne constitue pas une terre aride dans l’univers
scientifique. Elle est à la fois reine, servante et fille des sciences
de l’observation.
Gustave Choquet (1915–2006)
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Penot, JP. (2016). Encounters With Limits. In: Analysis. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-32411-1_2
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DOI: https://doi.org/10.1007/978-3-319-32411-1_2
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