upper semicontinuous collection (english) - meaning, definition, translation, pronunciation

Part of Speech

• Noun Phrase

Phonetic Transcription

• /ˈʌpər ˌsɛmɪkənˈtɪnjuəs kəˈlɛkʃən/

Meaning and Usage

• The term "upper semicontinuous collection" is a mathematical concept used primarily in topology and set theory. An upper semicontinuous collection of sets refers to a family of sets that exhibits a certain continuity property; specifically, for any point, the collection does not increase as you move "up" in terms of inclusion of points in the sets. This concept is important in various branches of mathematical analysis and is typically used in written contexts, especially in academic papers and textbooks.

• Frequency of Use: It is a specialized term more likely encountered in written academic or research-oriented contexts rather than in everyday oral speech.

Example Sentences

1. The researcher illustrated that the upper semicontinuous collection of sets can be used to establish convergence in certain functional spaces.

2. Исследователь продемонстрировал, что верхняя полуконтинуальная коллекция множеств может быть использована для установления сходимости в определённых функциях пространства.

3. In this topology, the upper semicontinuous collection provides a way to understand limit points more effectively.

4. В этой топологии верхняя полуконтинуальная коллекция предоставляет способ лучше понять предельные точки.

5. The proof relies heavily on the properties of the upper semicontinuous collection, which play a crucial role in ensuring the desired outcomes.

6. Доказательство во многом зависит от свойств верхней полуконтинуальной коллекции, которые играют решающую роль в обеспечении желаемых результатов.

Idiomatic Expressions

While "upper semicontinuous collection" does not commonly appear in idiomatic expressions, mathematical discourse often includes phrases that imply continuity and boundedness. Here are some idiomatic expressions related to continuity:

1. "To keep things in check"
2. We need an upper semicontinuous approach to keep things in check and ensure stability in this project.

3. Нам нужен верхний полуконтинуальный подход, чтобы держать всё под контролем и обеспечить стабильность в этом проекте.

4. "To draw the line"

5. When defining our upper semicontinuous collection, we must draw the line at excessive inclusivity.

6. Определяя нашу верхнюю полуконтинуальную коллекцию, мы должны провести грань на чрезмерной инклюзивности.

7. "To keep it balanced"

8. In mathematical proofs, it’s crucial to keep it balanced; an upper semicontinuous collection ensures we do just that.
9. В математических доказательствах крайне важно поддерживать баланс; верхняя полуконтинуальная коллекция гарантирует, что мы сделаем именно это.

Etymology

The term is derived from: - Upper: Middle English "uper", from Old English "ūpere", meaning 'above'. - Semicontinuous: A combination of "semi" (from Latin "semi-", meaning 'half') and "continuous" (from Latin "continuus", meaning 'uninterrupted'). - Collection: French "collection", from Latin "collectio", meaning 'a gathering'.

Synonyms and Antonyms

• Synonyms: Collection of upper semicontinuous sets, upper semi-continuity.
• Antonyms: Lower semicontinuous collection, discontinuous collection.

This term is quite specific and technical, hence synonyms and antonyms are used within a similarly formal mathematical context.