topology
/tə'pɔlədʤi/
Học thuậtThân thiện
Definition
- Noun:
- The branch of mathematics concerned with the properties of geometric figures that remain unchanged under continuous deformations: Topology studies spatial relationships and continuity, focusing on properties like connectedness and compactness rather than exact distances or angles.
- The arrangement or configuration of elements in a complex system, especially a communication network: In computing and engineering, topology describes how components are interconnected.
- The topographic study of a place, including its physical features and historical development as shaped by them: This usage relates to geography and landscape history.
- Regional anatomy, emphasizing the relationships between structures in a specific area of the body: In medicine, this refers to the study of bodily structures by region.
Usage Examples
- Noun (Mathematics):
- Understanding the topology of a shape helps mathematicians classify objects like knots and surfaces.
- A coffee mug and a doughnut are equivalent in topology because one can be deformed into the other.
- Noun (Computing/Networks):
- The network administrator changed the office topology from a bus to a star configuration.
- A mesh topology provides more redundancy than a ring topology.
- Noun (Geography/History):
- The book examines the topology of ancient Rome, showing how hills influenced its growth.
- Noun (Medicine):
- Surgeons must have an excellent knowledge of thoracic topology.
Advanced Usage
- "Algebraic topology": A major subfield using algebraic structures (like groups) to study topological spaces.
- Algebraic topology uses tools like homotopy groups to distinguish between spaces.
- "Network topology": The specific layout or structure of connections in a telecommunications or computer network.
- Choosing the right network topology is crucial for system performance and reliability.
- "Topology optimization": (In engineering) A mathematical method for optimizing material layout within a given design space.
- Topology optimization software helped design a lighter, stronger aircraft component.
Variants and Related Words
- Topological (adj): Relating to topology.
- The two shapes are topologically identical.
- Topologist (n): A mathematician specializing in topology.
- Topographical (adj): Relating to the physical features of an area. (Note: While related in some contexts, "topography" and "topology" are distinct; topography is concerned with precise elevation and mapping).
Synonyms
- Analysis situs: An older term for topology in mathematics.
- Rubber-sheet geometry: An informal name for the mathematical concept, highlighting the idea of continuous deformation.
- Configuration or Layout: For the network/system sense.
- Regional anatomy: For the medical sense.
Related Phrases
- "Continuous deformation": A core concept in mathematical topology, meaning a transformation that does not involve tearing or gluing.
- "Topological invariant": A property (like the number of holes) that remains constant under continuous deformations.
- Euler characteristic is a fundamental topological invariant.
- "Topological space": The fundamental object of study in topology, a set of points with a structure that defines concepts like nearness and continuity.
Noun
- the configuration of a communication network
- 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
- 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
- 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