The Eleventh Summer Conference on General Topology and Applications April 10-13, 1995 University of Southern Maine Portland, Maine

Digitally Continuous Homotopy by Laurence Boxer (Niagara University )

In (Rosenfeld, 1986), a natural analog of the usual \varepsilon-\delta definition of a continuous function is stated for digital pictures, and several properties of such digitally continuous functions are examined. Additional properties of digitally continuous functions are developed in (Boxer, 1994). In the current paper, we continue this work by developing properties of a digital version of homotopy. This gives us an alternative to the development of the digital fundamental group presented in (Kong, 1989) and (Kong, Roscoe, and Rosenfeld, 1992). We obtain digital analogs of many classical theorems concerning homotopy properties and fundamental groups.