Abstract
Abstract We discuss certain closure operators that generalize the Alexandroff topologies. Such a closure operator is defined for every ordinal α > 0 \alpha \gt 0 in such a way that the closure of a set A A is given by closures of certain α \alpha -indexed sequences formed by points of A A . It is shown that connectivity with respect to such a closure operator can be viewed as a special type of path connectivity. This makes it possible to apply the operators in solving problems based on employing a convenient connectivity such as problems of digital image processing. One such application is presented providing a digital analogue of the Jordan curve theorem.
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