ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note to entry: In a metric space, a set ${\displaystyle X}$ us open if each point ${\displaystyle x}$ in the set is contained in some small ball which is a subset of ${\displaystyle X}$ : ${\displaystyle \left[X\text{isopen}\right]\iff [x\in X]⟹[\exists \varepsilon >0϶\text{distance}(x,y)<\varepsilon ]⟹[y\in X]}$ . A topology is a set of subsets of a space which are considered open.