1.NounThe topology of the real number system generated by a basis which consists of all open balls (in the real number system), which are defined in terms of the one-dimensional Euclidean metric.
2.NounThe topology of a Euclidean space
R
n
{\displaystyle \mathbb {R} ^{n}}
such that any subset of that space is open (i.e. belonging to the topology) if it can be written as a union of open balls from that space.