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Topological: meaning, definitions and examples

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topological

 

[ˌtɒpəˈlɒdʒɪkəl ]

Definitions

Context #1 | Adjective

mathematics

Relating to or concerned with the topological properties of a space or geometric figure that are unaltered by elastic deformations such as stretching or twisting.

Synonyms

geometric, mathematical, structural.

Which Synonym Should You Choose?

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Word Description / Examples
topological

Used in mathematics and science to refer to properties that are preserved under continuous transformations such as stretching or bending, but not tearing or gluing.

  • The topological properties of the shape remain unchanged even when it's stretched
geometric

Used to describe anything related to geometry, which is the branch of mathematics that deals with the shapes, sizes, and properties of figures and spaces.

  • The geometric design of the building includes many triangular patterns
mathematical

Broadly used to describe anything related to mathematics, including concepts, theorems, models, and calculations.

  • The mathematical model helped predict the population growth over the next decade
structural

Commonly used to describe the arrangement and relations between the parts of a system, object, or conceptual framework. Often used in engineering and architecture.

  • The structural integrity of the bridge is crucial to its safety

Examples of usage

  • The topological study of knots and surfaces is a key area in mathematics.
  • Topological spaces are widely used in various branches of mathematics.
Context #2 | Adjective

computing

Relating to the arrangement of nodes or devices in a computer network.

Synonyms

arranged, connected, networked.

Which Synonym Should You Choose?

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Word Description / Examples
topological

Used in scientific and mathematical contexts to describe properties that are preserved through deformations, twistings, and stretchings. Also used in describing relationships and structures without necessarily referring to physical attributes.

  • In topology, a topological space is a set of points, each with a neighborhood
  • The topological properties of a shape remain constant even when it's distorted
  • The topological analysis of the map highlighted its most crucial connections
networked

Used primarily in a technical or organizational context where forming a network is involved, particularly in computing or social systems. Indicates that multiple entities are interactively connected.

  • The company's entire IT infrastructure is networked
  • The conference was a great opportunity for professionals to get networked
  • The sensors in the smart home are networked to offer better functionality
connected

Suitable for situations where indicating a relationship or linkage between two or more entities is required. This can be a physical connection or a conceptual one.

  • The two cities are connected by a high-speed train
  • All the computers in the office are connected to the same network
  • She felt deeply connected to her childhood memories
arranged

Used in everyday situations to describe something that has been put in a specific order or organized in a particular manner. Commonly used for physical items and schedules.

  • The books on the shelf were arranged alphabetically
  • She arranged the meeting for 3 PM
  • The flowers were beautifully arranged in the vase

Examples of usage

  • The topological structure of the network determines its efficiency and reliability.
  • Topological analysis helps in optimizing the performance of computer networks.

Interesting Facts

Etymology

  • The word 'topological' is derived from 'topology', which comes from the Greek words 'topos' meaning 'place' and 'logia' meaning 'study'.
  • The term 'topology' was first used in the 18th century, but it became more formalized in the 20th century with the work of mathematicians like Henri Poincaré.

Mathematics

  • Topology is often referred to as 'rubber-sheet geometry' because it doesn't concern itself with exact shapes, but with their properties when stretched or deformed.
  • One famous concept in topology is the 'Klein bottle', which is a one-sided surface where water poured in continually flows out without end.
  • Topology plays a crucial role in various mathematical fields, including algebraic topology, which involves the study of shapes as algebraic structures.

Art and Design

  • Some modern artists use topological concepts in their work, creating pieces that explore spatial relationships and forms, resembling objects that could 'change' their shape.
  • Artists like M.C. Escher incorporated topological principles in their artwork, creating impossible structures that challenge our perception of space.

Computer Science

  • In computer science, topological data analysis helps to uncover the structure of data, revealing patterns that are not immediately visible.
  • Networks, graphs, and the arrangements of connections between different nodes can often be studied using topological methods, impacting algorithms and data processing.

Physics

  • In modern physics, topology is significant in quantum computing and condensed matter physics, where the 'topological phase' of a material offers unique properties.
  • Certain topological materials can conduct electricity on their surface while acting as insulators in their bulk, leading to revolutionary technological advances.

Translations

Translations of the word "topological" in other languages:

🇵🇹 topológico

🇮🇳 टोपोलॉजिकल (टोपोलॉजी से संबंधित)

🇩🇪 topologisch

🇮🇩 topologi

🇺🇦 топологічний

🇵🇱 topologiczny

🇯🇵 位相的 (いそうてき)

🇫🇷 topologique

🇪🇸 topológico

🇹🇷 topolojik

🇰🇷 위상적인 (위상과 관련된)

🇸🇦 طوبولوجي

🇨🇿 topologický

🇸🇰 topologický

🇨🇳 拓扑的 (tàpū de)

🇸🇮 topološki

🇮🇸 toppfræðilegur

🇰🇿 топологиялық

🇬🇪 ტოპოლოგიური

🇦🇿 topoloji

🇲🇽 topológico

Word Frequency Rank

At position #14,111, this word is part of sophisticated English vocabulary. It's useful for academic or professional contexts where precise language is needed.