FIBRATION Meaning and
Definition
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Fibration is a term predominantly used in the field of mathematics, specifically in topology and algebraic geometry. It refers to a fundamental concept that describes a mathematical structure or mapping between two spaces.
In simple terms, a fibration is a continuous map or function that relates one space (known as the total space) to another space (known as the base space) in a specific manner. The fibration can be visualized as a bundle of fibers, where each fiber is a copy of a particular space. These fibers are connected together in a coherent way, giving rise to the total space.
A key characteristic of a fibration is that it preserves certain topological properties between the total and base spaces. For example, if one point in the base space is changed, the corresponding fiber will also be modified in a consistent manner. This property ensures that the fibration maps elements from the base space to the total space continuously and smoothly.
Fibrations find applications in various branches of mathematics, physics, and engineering. They offer a powerful tool for studying and understanding the relationships and structures between different spaces. By capturing the notion of a bundle of fibers, fibrations enable mathematicians to explore connections between spaces and investigate important properties such as dimensionality, homotopy, and deformation.
In summary, a fibration is a mathematical concept that relates one space to another in a systematic way through a continuous mapping. It provides a framework for studying the interplay between spaces and has significant implications in diverse areas of mathematics.
Common Misspellings for FIBRATION
- dibration
- cibration
- vibration
- gibration
- tibration
- ribration
- fubration
- fjbration
- fkbration
- fobration
- f9bration
- f8bration
- fivration
- finration
- fihration
- figration
- fibeation
- fibdation
- fibfation
- fibtation
Etymology of FIBRATION
The word "fibration" derives from the Latin word "fibra", which means "fiber" or "thread". The term "fibration" was coined in mathematics to describe a certain type of structure that resembles fibers or threads. In topology and algebraic geometry, a fibration refers to a mapping between topological or algebraic spaces such that each point in the target space has a neighborhood that can be continuously "fibred" over a corresponding point in the source space. This term was introduced by Samuel Eilenberg and Norman Steenrod in the 1950s to describe a certain kind of mapping more general than a fiber bundle.
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