Generalized Metric Spaces
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The basic problem of the principle of mutual classifications of spaces and mappings is that, under which classes of mappings certain topological properties remain unchanged (see Question 2.0.6). One of the central topics of this chapter is to determine the given classes of generalized metric spaces are preserved by which kinds of mappings. Therefore, we must fully investigate various properties of generalized metric spaces. One of the most wonderful content of this chapter i.e. seeking the characterizations of these generalized metric spaces is particularly important.