structural:reformatting, structural:scholar_edition
Other definitions

There are many other equivalent ways to define a topological space: in other words the concepts of neighbourhood, or that of open or closed sets can be reconstructed from other starting points and satisfy the correct axioms.

Another way to define a topological space is by using the Kuratowski closure axioms, which define the closed sets as the fixed points of an operator on the power set of X. {\displaystyle X.}

A net is a generalisation of the concept of sequence. A topology is completely determined if for every net in X {\displaystyle X} the set of its accumulation points is specified.