20 best topology books of all time (update 2022)
20 Best Topology Books of All Time (Update 2022)
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Topology is brach of mathematics that preserved through deformations, bendings, twistings, stretchings and shtrinking of objects. Tearing however is not allowed. The main topics of interest in topology are the properties that remain unchanged by such continuous deformations.
Topology is sometimes called "rubber-sheet geometry" because the objects can be stretched and contracted like rubber, but cannot be broken.
For example, a square can be deformed into a circle without breaking it, but a figure 8 cannot.
Hence a square is topologically equivalent to a circle, but different from a figure 8.
picture: square, circle, figure 8.
Topology & Geometry
Topology, while similar to geometry, differs from geometry in that geometrically equivalent objects often share numerically measured quantities, such as lengths or angles, while topologically equivalent objects resemble each other in a more qualitative sense.
General topology overlaps with another important area of topology called algebraic topology.
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