topologic

Thân thiện

A mathematician draws a topologic diagram on a chalkboard.

Definition

1. Adjective:
   • Relating to topology: Pertaining to the mathematical study of the properties of geometric figures or spatial structures that remain unchanged under continuous deformations, such as stretching or bending, but not tearing or gluing. It describes concepts, spaces, or properties within this field of mathematics.

Usage Examples

• Adjective:
  • The two shapes are considered identical from a topologic perspective because one can be continuously deformed into the other.
  • Understanding the topologic properties of a network is crucial for analyzing its resilience.
  • This theorem addresses a fundamental topologic characteristic of the space.

Advanced Usage

• "Topologic invariant": A property of a topological space that remains unchanged under homeomorphisms (continuous deformations).
  • Euler characteristic is a key topologic invariant.
• "Topologic space": A set equipped with a structure that defines the notion of neighborhoods, allowing the formalization of concepts like continuity and convergence.
  • The definition of continuity is grounded in the concept of a topologic space.

Variants and Related Words

• Topological (adj): The more common adjectival form, fully synonymous with "topologic."
  • Topological data analysis is a growing field.
• Topology (n): The branch of mathematics itself.
  • She is writing her thesis on algebraic topology.
• Topologist (n): A mathematician specializing in topology.
  • The problem was solved by a renowned topologist.

Synonyms

• Topological: (Direct synonym, more frequently used).

Related Phrases

• Topologic equivalence: The relationship between two spaces that can be transformed into one another through a continuous deformation (a homeomorphism).
  • A coffee mug and a doughnut are in topologic equivalence.

Học thuật

Adjective

1. of or relating to topology

Từ đồng nghĩa

• topological