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closed set

American  

noun

Mathematics.

  1. a set that contains all of its accumulation points, as the set of points on and within a circle; a set having an open set as its complement.

closed set British  

noun

  1. a set that includes all the values obtained by application of a given operation to its members

  2. (in topological space) a set that contains all its own limit points

"Collins English Dictionary — Complete & Unabridged" 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Example Sentences

Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.

And Barrett wondered where this closed set came from.

From Slate • Apr. 1, 2026

Were those sequences filmed on a closed set?

From Los Angeles Times • Apr. 29, 2025

On a closed set of about eight people, with music blasting to pump them up, Corrin and O’Connell cut loose.

From New York Times • Dec. 2, 2022

Badu tweeted that it was filmed "guerrilla style, no crew, 1 take, no closed set, no warning" in just two minutes, in the Dealey Plaza district of Dallas, Texas.

From BBC • May 9, 2018

They turned to a closed set of double doors.

From "Book Scavenger" by Jennifer Chambliss Bertman

Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.