biregular mapping (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/bɪˈrɛɡjʊlər ˈmæpɪŋ/

Meaning and Usage

A biregular mapping is a mathematical concept referring to a type of mapping or function between two sets (typically in the context of topology or algebra) where both sets have an additional structure (like a topology or algebraic structure) that is preserved under the mapping. It generally describes a situation where both the forward and the inverse mappings maintain certain regularities, such as continuity or smoothness.

Biregular mapping is used primarily in advanced mathematics, more specifically in fields such as topology, differential geometry, and algebraic topology. Its usage is more common in written academic texts than in everyday oral communication due to its specialized nature.

Example Sentences

1. Biregular mapping is essential in studying the properties of topological spaces and their mappings.

2. Translation: Бирегулярное отображение имеет решающее значение для изучения свойств топологических пространств и их отображений.

3. The researchers found that a biregular mapping between the two geometrical figures revealed interesting similarities.

4. Translation: Исследователи обнаружили, что бирегулярное отображение между двумя геометрическими фигурами выявило интересные сходства.

5. In the course on topology, we covered the concept of biregular mapping extensively.

6. Translation: На курсе по топологии мы подробно рассмотрели концепцию бирегулярного отображения.

Idiomatic Expressions

While "biregular mapping" does not frequently occur in idiomatic expressions, we can explore its context in mathematical discourse:

1. "To draw a map is not as easy as creating a biregular mapping."

2. Translation: Нарисовать карту не так просто, как создать бирегулярное отображение.

3. "In mathematics, one must often go beyond intuition to understand the concept of biregular mapping."

4. Translation: В математике часто нужно выходить за пределы интуиции, чтобы понять концепцию бирегулярного отображения.

5. "Without a solid grasp of the basics, one cannot appreciate the nuances of biregular mapping."

6. Translation: Без твердого понимания основ невозможно оценить нюансы бирегулярного отображения.

Etymology

The term "biregular" comes from the prefix "bi-", meaning "two," and "regular," which comes from the Latin "regularis," meaning "made according to rule." "Mapping" is derived from the Old French "mappe," referring to a representation of space or arrangement.

Synonyms and Antonyms

Synonyms: - Regular mapping - Biholomorphic mapping (in a specific context)

Antonyms: - Irregular mapping - Non-continuous mapping

Biregular mapping is a specialized term primarily situated in mathematical conversations, emphasizing its intricate role in understanding structures and functions in higher-level mathematics.