![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/Simply_connected%252C_connected%252C_and_non-connected_spaces.svg/640px-Simply_connected%252C_connected%252C_and_non-connected_spaces.svg.png&w=640&q=50)
Connected space
Topological space that is connected / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Path-connected?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces.
Connected and disconnected subspaces of R²
From top to bottom: red space A, pink space B, yellow space C and orange space D are all connected spaces, whereas green space E (made of subsets E1, E2, E3, and E4) is disconnected. Furthermore, A and B are also simply connected (genus 0), while C and D are not: C has genus 1 and D has genus 4.
A subset of a topological space is a connected set if it is a connected space when viewed as a subspace of
.
Some related but stronger conditions are path connected, simply connected, and -connected. Another related notion is locally connected, which neither implies nor follows from connectedness.