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topology    
n. 地志学,拓扑数学,局部解剖学

地志学,拓扑数学,局部解剖学

topology
拓扑

topology
拓扑学 布局

topology
n 1: topographic study of a given place (especially the history
of the place as indicated by its topography); "Greenland's
topology has been shaped by the glaciers of the ice age"
2: the study of anatomy based on regions or divisions of the
body and emphasizing the relations between various structures
(muscles and nerves and arteries etc.) in that region [synonym:
{regional anatomy}, {topographic anatomy}, {topology}]
3: the branch of pure mathematics that deals only with the
properties of a figure X that hold for every figure into
which X can be transformed with a one-to-one correspondence
that is continuous in both directions [synonym: {topology},
{analysis situs}]
4: the configuration of a communication network [synonym:
{topology}, {network topology}]

Topology \To*pol"o*gy\, n. [Gr. ? place -logy.]
The art of, or method for, assisting the memory by
associating the thing or subject to be remembered with some
place. [R.]
[1913 Webster]

2. a branch of mathematics which studies the properties of
geometrical forms which retain their identity under
certain transformations, such as stretching or twisting,
which are homeomorphic. See also {topologist}.
[PJC]

3. configuration, especially in three dimensions; -- used, e.
g. of the configurations taken by macromolecules, such as
superhelical DNA.
[PJC]


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  • Topology - Wikipedia
    The term topology also refers to a specific mathematical idea central to the area of mathematics called topology Informally, a topology describes how elements of a set relate spatially to each other
  • Topology | Types, Properties Examples | Britannica
    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
  • What is Topology? - Wayne State University
    In topology, any continuous change which can be continuously undone is allowed So a circle is the same as a triangle or a square, because you just 'pull on' parts of the circle to make corners and then straighten the sides, to change a circle into a square
  • Introduction to Topology - Cornell University
    A topology on a set X is given by defining “open sets” of X Since closed sets are just exactly complement of open sets, it is possible to define topology by giving a collection of closed sets
  • TOPOLOGY Definition Meaning - Merriam-Webster
    The meaning of TOPOLOGY is topographic study of a particular place; specifically : the history of a region as indicated by its topography How to use topology in a sentence
  • Introduction to Topology | Mathematics | MIT OpenCourseWare
    Introduction to Topology Course Description This course introduces topology, covering topics fundamental to modern analysis and geometry
  • What is Topology? | Pure Mathematics | University of Waterloo
    Topology studies properties of spaces that are invariant under any continuous deformation It is sometimes called "rubber-sheet geometry" because the objects can be stretched and contracted like rubber, but cannot be broken
  • Topology -- from Wolfram MathWorld
    Topology began with the study of curves, surfaces, and other objects in the plane and three-space One of the central ideas in topology is that spatial objects like circles and spheres can be treated as objects in their own right, and knowledge of objects is independent of how they are "represented" or "embedded" in space
  • Algebraic topology - Wikipedia
    Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence
  • Topology | Brilliant Math Science Wiki
    Topology is the study of properties of geometric spaces which are preserved by continuous deformations (intuitively, stretching, rotating, or bending are continuous deformations; tearing or gluing are not)





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