Banach Sets Stage for Abstract Spaces

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Article abstract: On the basis of his observation that many mathematical structures had features in common with ordinary three-dimensional structures, Stefan Banach constructed abstract spaces of tremendous beauty and utility.

Classical Geometries

A one-dimensional space can be visualized as a straight line. To locate points on that line, one selects a point on the line and calls it the “origin.” Other points can be located relative to the origin. One direction from the origin is labeled positive; the other, negative. A point on the line is specified...

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