Topological Analysis 175 浏览 0关注

Topology (from the Greek language|Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with the most basic properties of space, such as connectedness. More precisely, topology studies properties that are preserved under Continuous function|continuous deformations, including stretching and bending, but not tearing or gluing. The exact mathematical definition is given below. Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, which was referred to in Latin as the geometria situs (“geometry of place”) or analysis situs (Greek-Latin for “picking apart of place”). This later acquired the modern name of topology. By the middle of the 20th century, topology had become an important area of study within mathematics. Topology has...
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