The relations between ultracompactness of topological spaces and ultraClosedness of mappings, are further studied in this paper. The properties of ultraclosed mappings are displayed. An expression of D-limits of nets ...The relations between ultracompactness of topological spaces and ultraClosedness of mappings, are further studied in this paper. The properties of ultraclosed mappings are displayed. An expression of D-limits of nets in a space is given by using closure operation. The notions of ultracontinuity and ultraperfectness of mappings are presented on the basis of [6] and [9], and relations between these mappings are discussed. The main work of this paper is the study of cartesian products and diagonals of mapping. And a theory on ultraclosed mappings is set up.展开更多
文摘The relations between ultracompactness of topological spaces and ultraClosedness of mappings, are further studied in this paper. The properties of ultraclosed mappings are displayed. An expression of D-limits of nets in a space is given by using closure operation. The notions of ultracontinuity and ultraperfectness of mappings are presented on the basis of [6] and [9], and relations between these mappings are discussed. The main work of this paper is the study of cartesian products and diagonals of mapping. And a theory on ultraclosed mappings is set up.
