# Open set

From Encyclopedia of Mathematics

*in a topological space*

An element of the topology (cf. Topological structure (topology)) of this space. More specifically, let the topology of a topological space be defined as a system of subsets of the set such that: 1) , ; 2) if , , then ; and 3) if , , then . The open sets in the space are then the elements of the topology and only them.

#### Comments

#### References

[a1] | R. Engelking, "General topology" , Heldermann (1989) |

**How to Cite This Entry:**

Open set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Open_set&oldid=18168

This article was adapted from an original article by B.A. Pasynkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article