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Topology: Properties
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Topology (Greek [T]opos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. When the discipline was first properly founded, in the early years of the 20th century, it was still called geometria situs (Latin geometry of place) and analysis situs (Latin analysis of place). From around 1925 to 1975 it was the most important growth area within mathematics.
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Topology, the youngest and most sophisticated branch of geometry, focuses on the properties of geometric objects that remain unchanged upon continuous deformation—shrinking, stretching, and folding, but not tearing. The continuous development of topology dates from 1911, when the Dutch mathematician L.E.J.
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Topology is ... concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms). Two figures that can be deformed one into the other are called homeomorphic, and are considered to be the same from the topological point of view. For example a solid cube and a solid sphere are homeomorphic.
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