On Near-compact Images And Almost S-images Of Metric Spaces

Non-isolated points and non-sequentially-open points are two kinds of special points in a topological space.By using the family properties of two kinds of special point sets,we can discuss near-compact images,almost s-images of metric spaces and their metrizable problems.The main results in this dissertation are the following:In Chapter 2,we introduce the notion of a near-compact mapping,study basic relations among almost-compact mappings,near-compact mappings and boundary-compact mappings,and obtain internal characterizations of sequence-covering near-compact images of metric spaces.We also discuss the relations among the spaces under these kinds of compact images of metric spaces.In Chapter 3,we introduce the notion of a near s-mapping,study basic relations among almost s-mappings,near s-mappings and boundary-s-mappings,and obtain internal characterizations of open almost s-images of metric spaces.We also discuss the relations among the spaces under these kinds of s-images of metric spaces.In Chapter 4,we discuss that the properties of spaces with a network which is ?-locally finite at non-isolated points,and obtain some new characterizations of ?-spaces,(?)-spaces and metric spaces by the properties of collections at non-isolated points.The closed s-mapping theorem of metric spaces is also obtained.