Topological Spaces and Continuous Functions

The articles [4], [2], [5], [6], [1], and [3] provide the notation and terminology for this paper. We consider topological structures as extensions of 1-sorted structure as systems 〈 a carrier, a topology 〉, where the carrier is a set and the topology is a family of subsets of the carrier. In the sequel T is a topological structure. Let I1 be a topological structure. We say that I1 is topological space-like if and only if the conditions (Def. 1) are satisfied.