Closure operations for digital topology

We study certain generalized topological structures, called closure operations, that are associated with -ary relations ( ¿ 1 an ordinal). It turns out that some of these structures are well-behaved with respect to connectedness and so are suitable for applications in digital topology. In particular, for any natural number n¿ 1 we ,nd an appropriate closure operation on Z, which is associated with a special n-ary relation on Z. In the case n = 2 this closure operation coincides with the known Khalimsky topology. c © 2002 Elsevier B.V. All rights reserved.