In mathematics, and especially
general topology, the
Euclidean topology is an example of a topology given to the set of
real numbers, denoted by
R. To give the set
R a topology means to say which
subsets of
R are "
open", and to do so in a way that the following
axioms are met:
- The union of open sets is an open set.
- The finite intersection of open sets is an open set.
- The set R and the empty set Ø are open sets.