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
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