Topological Meaning: Definition, Examples, and Translations
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topological
[หtษpษหlษdสษชkษl ]
Definitions
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?
| 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.
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| 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.
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| mathematical |
Broadly used to describe anything related to mathematics, including concepts, theorems, models, and calculations.
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| 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.
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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.
computing
Relating to the arrangement of nodes or devices in a computer network.
Synonyms
arranged, connected, networked.
Which Synonym Should You Choose?
| 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.
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| 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.
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| 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.
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| 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.
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Examples of usage
- The topological structure of the network determines its efficiency and reliability.
- Topological analysis helps in optimizing the performance of computer networks.
Translations
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Interesting Facts
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.
Origin of 'topological'
Main points about word origin
- 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 Poincarรฉ.
The term 'topological' originated in the early 20th century from the combination of 'topo-' meaning place or location, and '-logical' indicating a relation to logic or study. It gained popularity in mathematics and later expanded to other fields like computer science. The concept of topological spaces and structures has become fundamental in various scientific disciplines.