Open set

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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.



[a1] R. Engelking, "General topology" , Heldermann (1989)
How to Cite This Entry:
Open set. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by B.A. Pasynkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article