In mathematics, an open set is a generalization of an open interval in the real line. In a metric space (a set along with a distance defined between any...
28 KB (4,574 words) - 13:12, 16 April 2024
In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed. That this is possible may...
5 KB (785 words) - 11:24, 30 January 2024
{\displaystyle S} of a topological space X {\displaystyle X} is called a regular open set if it is equal to the interior of its closure; expressed symbolically,...
3 KB (570 words) - 18:45, 7 February 2023
Glossary of topology (redirect from Semi-open set)
open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of...
55 KB (7,583 words) - 12:00, 19 April 2024
mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations...
12 KB (1,778 words) - 13:47, 9 May 2024
mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its...
11 KB (1,952 words) - 03:13, 26 December 2023
Topological space (redirect from Open set topology)
a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is...
28 KB (4,043 words) - 16:49, 8 May 2024
dense sets need not contain any non-empty open set. The intersection of two dense open subsets of a topological space is again dense and open. The empty...
12 KB (1,911 words) - 13:33, 2 May 2024
more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function f : X → Y {\displaystyle...
31 KB (5,306 words) - 18:47, 14 December 2023
Cover (topology) (redirect from Cover (set theory))
cover of a set is a subset of the cover that also covers the set. A cover is called an open cover if each of its elements is an open set. Covers are...
8 KB (1,376 words) - 07:40, 25 February 2024