Limit and continuity are the most important concepts in the theory of the real number set, and the real number set can be regarded as a special topological space, so how to define the limit and con-tinuity of the function from the topological space to the real number fi...MORE Limit and continuity are the most important concepts in the theory of the real number set, and the real number set can be regarded as a special topological space, so how to define the limit and con-tinuity of the function from the topological space to the real number field is of great research sig-nificance. In this pape...