Meaning: A "bundle isomorphism" is a mathematical concept in the field of category theory and differential geometry. It refers to an isomorphism between two fiber bundles that preserves the structure of the fibers. In simpler terms, it indicates that there is a way to map one bundle onto another in a structure-preserving manner, where the fibers correspond to each other in a way that respects their topological and algebraic properties.
Usage: The term "bundle isomorphism" is predominantly used in academic and professional contexts, particularly in mathematics and theoretical physics. It is less common in everyday spoken or written English, as it relates to specialized fields that require a certain level of understanding of advanced concepts.
Frequency of Use: This term is more frequently used in written contexts, especially in academic papers, textbooks, and conference discussions.
Концепция изоморфизма связок играет ключевую роль в изучении векторных связок.
To prove a property of the manifold, one must demonstrate the existence of a bundle isomorphism.
Чтобы доказать свойство многообразия, необходимо продемонстрировать существование изоморфизма связок.
In advanced calculus, we often encounter examples of bundle isomorphism when discussing differential forms.
While "bundle isomorphism" does not appear in idiomatic expressions, there are other phrases involving "bundle" in English that could provide useful context:
"Пакет радости" относится к новорожденному ребенку.
"Bundled up" means to dress warmly, particularly in layers.
"Упаковаться тепло" означает одеваться тепло, особенно в несколько слоев.
"In a bundle" implies being grouped together, often in a chaotic way.
"В груде" подразумевает нахождение вместе, часто в хаотичном состоянии.
"Don't throw the baby out with the bathwater" suggests not to discard something valuable while getting rid of the unnecessary.
"Не выбрасывайте младенца с водой для ванны" предполагает не выбрасывать что-то ценное при избавлении от ненужного.
"A bundle of nerves" refers to a person who is extremely anxious or stressed.
The term "bundle" has origins in Old English "bynþ," which means "to bind." The term "isomorphism" comes from Greek roots, where "iso-" means "equal" and "morphe" means "form." Together, they signify a form-preserving map.
Synonyms: - Isomorphism - Structure-preserving map
Antonyms: - Isomorphism (when referring to a lack of such structure-preserving relationships) - Non-isomorphic bundles
Overall, "bundle isomorphism" is a specialized term most applicable to advanced studies in mathematics and related fields, highlighting its unique structural properties within algebraic and topological contexts.