Closed graph property and Khalimsky spaces

In the following text for Khalimsky n-dimensional space Kn we show self-map f:Kn →Kn has closed graph if and only if there exist integers λ۱,...,λn such that f is a constant map with value (۲λ۱,...,۲λn). We also show each self--map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples.

کلیدواژه ها:

Alexandroff space ، Closed graph ، Digital topology ، Khalimsky spaces