weakly open (english) - meaning, definition, translation, pronunciation

Part of Speech

The term "weakly open" functions as an adjective in the English language.

Phonetic Transcription

/ˈwiːkli ˈoʊpən/

Meaning and Usage

"Weakly open" is primarily used in mathematical contexts, especially in topology. It describes a certain type of openness of a set in a topological space, indicating that for every point in the set, there is a neighborhood that intersects with the set in a weakly defined manner. This term can often appear in written contexts, particularly in academic papers, textbooks, and specialized courses dealing with advanced mathematics.

Example Sentences

1. The topological space is said to be weakly open if every point has a weakly open neighborhood.

2. Translation: Пространство топологии называется слабо открытым, если у каждой точки есть слабо открытое окружение.

3. In functional analysis, weakly open sets provide insight into the convergence of sequences.

4. Translation: В функциональном анализе слабо открытые множества дают представление о сходимости последовательностей.

5. The concept of weakly open sets is essential in understanding the properties of a given space.

6. Translation: Концепция слабо открытых множеств важна для понимания свойств данного пространства.

Idiomatic Expressions

Although "weakly open" is a specialized term that is less commonly used in idiomatic expressions, the concept of "open" can be found in several expressions:

1. Open the door to new possibilities.

2. Translation: Откройте дверь новым возможностям.

3. An open book.

4. Translation: Открытая книга.

5. Open your heart.

6. Translation: Откройте свое сердце.

7. Open a can of worms.

8. Translation: Открыть консервную банку червей. (приближенное значение: создать дополнительные проблемы.)

9. Open up a dialogue.

10. Translation: Открыть диалог.

11. Open the floodgates.

12. Translation: Открыть шлюзы.

Etymology

The term "weakly" comes from the root word "weak," which means lacking strength or vigor. The suffix "-ly" turns the adjective into an adverb. "Open" originates from the Old English "āpen," meaning not closed or obstructed. Together, "weakly open" emerges in mathematical language as a specification of how openness is defined in a more flexible manner.

Synonyms and Antonyms

Synonyms: - Loosely defined - Mildly open

Antonyms: - Strongly open - Closed

In summary, "weakly open" is a specialized term in topology that reflects a unique characteristic of certain sets in mathematical fields. It is predominantly used in written academic texts rather than in everyday language.