a set closure

USAGE SUMMARY

The phrase "a set closure" is correct and usable in written English.
It can be used in contexts related to mathematics, computer science, or discussions about topology, where it refers to the closure of a set in a given space. Example: "In topology, a set closure is essential for understanding the properties of closed sets."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

Every class has a set closure.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

A set of closure relations was collected at the Helmholtz-Zentrum Dresden-Rossendorf that represents the best available knowledge.

Petroleum

The present work applies a set of closure relations that was previously used with good success to describe bubbly flows in pipes and bubble columns.

Chemical Engineering Science

A set of closure relations has been collected at the Helmholtz-Zentrum Dresden-Rossendorf that represents the best available knowledge and may serve as a baseline model for further investigations.

Chemical Engineering Science

First of all, we recall the following definitions: A nowhere dense subset of a topological space is a set whose closure has an empty interior in the topological space; that is, it contains no open neighbourhood of its elements in the topological space.

Fixed Point Theory and Applications

This set of generalized Ornstein Zernike equations must be supplemented by a set of closure relations.

Colloid and Polymer Science

The notion of fuzzy set closure is introduced to compare two fuzzy sets whose domain of values is a taxonomy.

Fuzzy Sets and Systems

A set of closures for two-fluid modelling of adiabatic bubbly flows has been defined as baseline model, which provides a common basis for further improvement and development.

Chemical Engineering Science

We denote by and, the set of positive integers and the closure (weak closure) of a set in, respectively.

Fixed Point Theory and Applications

We denote by ℕ and cl(M) (wcl(M)), the set of positive integers and the closure (weak closure) of a set M in X, respectively.

Fixed Point Theory and Applications

New high quality experimental data for the fluid dynamics of a bubble column are used to validate a baseline set of closure relations for bubbly flows.

International Journal of Multiphase Flow

Expert writing Tips

Best practice

When using "a set closure", ensure the context clearly indicates the type of closure being discussed, especially in mathematical or topological contexts. If the audience is not familiar with the concept, provide a brief explanation or definition.

Common error

Avoid using "a set closure" loosely without a clear mathematical or logical context. This phrase is specific and should not be used as a general term for completion or finality.

Linguistic Context

The phrase "a set closure" functions as a noun phrase that identifies a specific mathematical concept. As Ludwig AI confirms, it’s used to describe the closure operation applied to a set.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "a set closure" is a technically precise phrase primarily used within mathematical and scientific contexts to describe the concept of a set extended to include its limit points. As Ludwig confirms, it's grammatically sound, though its usage is relatively rare and specialized. When writing, it's important to ensure the context clearly indicates the mathematical or logical domain being discussed. Consider alternatives like "the closure of a set" for stylistic variation while maintaining the intended meaning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

closure of a set

Reverses the order and emphasizes the action of closure rather than the resulting entity being a set's property.

set's topological closure

Specifies the type of closure within the context of topology.

deductive closure of a set

Highlights that the closure is in the context of deductive reasoning, clarifying the type of closure.

the smallest closed set containing

Describes the closure by its defining property.

topological boundary of a set

Focuses on the boundary, which is related to the closure but emphasizes the edge of the set.

limit points of a set

Highlights the points that belong to the closure of a set.

adherence of a set

Uses a less common term ("adherence") that is synonymous with closure in some contexts.

the closed superset

Highlights that the closure is a larger set that contains the original set and is closed.

complete closure of the set

Adds the adjective "complete" to modify closure.

the hull of a set

Employs a different term that indicates the outer boundary or smallest containing structure.

FAQs

How is "a set closure" used in mathematics?

In mathematics, "a set closure" refers to the smallest closed set containing a given set. It includes the original set and all its limit points. It's fundamental in topology and analysis for defining completeness and convergence.

What is the difference between "a set closure" and "the closure of a set"?

"A set closure" and "the closure of a set" are essentially synonymous. The choice between them often depends on stylistic preference or the specific context of the discussion. In most cases, they are interchangeable.

What are some practical applications of understanding "a set closure"?

Understanding "a set closure" is crucial in fields like image processing, where it's used for morphological operations to fill gaps in images, and in database theory, where it helps in defining relational completeness.

Where can I find more information about "a set closure"?

More information can be found in textbooks on topology, real analysis, and set theory. Online resources like the Stanford Encyclopedia of Philosophy or academic journals focusing on mathematics can also provide detailed explanations.