Author’s summary: “In this paper, we introduce the notions of compact closure and compact interior for sets in topological spaces and the notions of transfer compact closedness and transfer compact openness for mappings. By using these notions, we prove some new H-KKM type theorems which generalize the most of known H-KKM and F-KKM type theorems in the literature. As applications, we obtain some new generalizations of the Ky Fan type geometric property of H-spaces, coincidence theorems and minimax inequality in H-spaces.
We also give some new existence theorems of maximal elements for preference relations in H-spaces which generalize the recent results of G. Tian [J. Math. Anal. Appl. 170, No. 2, 457-471 (1992; Zbl 0767.49007)]”.