โ Scribed by D. Buhagiar; T. Miwa; B.A. Pasynkov
No coin nor oath required. For personal study only.
In this paper we define and study MT-maps, which are the fibrewise topological analogue of metrizable spaces, i.e., the extension of metrizability from the category Top to the category Top Y . Several characterizations and properties of MT-maps are proved. The notion of an MT-space as an MT-map preimage of a metrizable space is introduced. Examples of MT-spaces and their relation with M-spaces are given. Finally it is deduced that an MT-space with a G ฮด -diagonal is metrizable.
๐ SIMILAR VOLUMES
We prove that for a metrizable space X the following are equivalent: (i) the free Abelian topological group A(X) is the inductive limit of the sequence {A n (X): n โ N}, where A n (X) is formed by all words of reduced length n; (ii) X is locally compact and the set of all non-isolated points of X is
The purpose of this note is to give some remarks and questions on metrizability and generalized metric spaces.
The concept of a 2-metric space hw been investigated by 5. G~ELER in a seriea of papers [6]-[S]. Other papers dealing with 2-metric spaces are [3]-[S], [lo], and [ 123. In this note several fixed point theorems a m proved for contractive mappings in a 2-metric space. The contradive definitions used