closed set: meaning, definition, pronunciation and examples
C1Formal, Academic, Technical
Quick answer
What does “closed set” mean?
A limited, fixed group of items, members, or categories where no new additions are allowed.
Audio
Pronunciation
Definition
Meaning and Definition
A limited, fixed group of items, members, or categories where no new additions are allowed.
In various disciplines (mathematics, linguistics, computing), a well-defined collection of elements with a fixed boundary; something that is not open to expansion or new members.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. The term is used identically in academic and technical registers.
Connotations
Slight nuance: in UK academic contexts, it might be more commonly associated with pure mathematics and linguistics; in US contexts, also heavily used in computer science and data science.
Frequency
Equally low-frequency in general discourse, but standard and common in relevant technical fields in both varieties.
Grammar
How to Use “closed set” in a Sentence
[The/This/That] + is/forms/constitutes + a closed set.A closed set of + [noun phrase] + exists/is defined.We treat/consider X as a closed set.Vocabulary
Collocations
Examples
Examples of “closed set” in a Sentence
verb
British English
- The committee decided to close the set of candidates early.
- We need to close the set of possible outcomes before modelling.
American English
- The algorithm closes the set of visited nodes.
- Let's close the set of variables under consideration.
adverb
British English
- The elements were defined closed-set, not open-ended.
- (Rare usage)
American English
- The data is organized closed-set, unlike an open database.
- (Rare usage)
adjective
British English
- It's a closed-set examination, meaning you must answer from a fixed list of topics.
- The phonology class studied closed-set lexical items.
American English
- We are working with a closed-set system of axioms.
- The debate used a closed-set list of approved sources.
Usage
Meaning in Context
Business
Rare. Might refer to a 'closed set of vendors' approved for procurement.
Academic
Primary use. In mathematics (topology), linguistics (phonology: closed class of words), and logic.
Everyday
Very rare. Could describe an exclusive social group not accepting new friends.
Technical
Common in mathematics, computer science (data structures, automata theory), and formal linguistics.
Vocabulary
Synonyms of “closed set”
Strong
Neutral
Weak
Vocabulary
Antonyms of “closed set”
Watch out
Common Mistakes When Using “closed set”
- Using 'close set' (missing the -d).
- Confusing with 'close-set' (hyphenated adjective meaning positioned closely together).
- Using it in informal contexts where 'limited selection' or 'fixed list' would be clearer.
FAQ
Frequently Asked Questions
The set of playing cards in a standard deck (52 cards). It is fixed; you don't add new cards to the standard rules.
In topology, yes, they are complementary concepts. In general language, the opposite is more like 'open-ended list' or 'expanding group'.
Yes. For example, the set of all integers is infinite, but in certain mathematical contexts (like within the real numbers with standard topology), it is not considered a closed set. However, the set of all points where x² + y² ≤ 1 (a filled circle) is infinite and closed.
In linguistics (e.g., grammar), it refers to a small, fixed word class like pronouns or prepositions, where new members are rarely added. In mathematics, it's a formal set-theoretic/topological concept based on boundaries and limit points, not necessarily small or lexical.
Closed set is usually formal, academic, technical in register.
Closed set: in British English it is pronounced /ˌkləʊzd ˈset/, and in American English it is pronounced /ˌkloʊzd ˈsɛt/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “A closed shop (related concept in labour unions)”
- “A closed circle”
Learning
Memory Aids
Mnemonic
Think of a CLOSED SET like a CLOSED SOCIETY: the door is shut (closed) to new members, so the group (set) is fixed and complete.
Conceptual Metaphor
CONTAINER (with a sealed lid), EXCLUSIVE CLUB, COMPLETE INVENTORY.
Practice
Quiz
In which field is the term 'closed set' LEAST likely to be used in its technical sense?