A study on dimension of continuous mappings
Abstract
In Dimension Theory, there are “mapping theorems” establishing
relationships between the dimensions of the domain and range of a continuous mapping. Most of the theorems deal with mappings that satisfy additional conditions such as being closed mappings. In the “environment” of such studies, dimensions of continuous mappings have been also studied. In this paper, we introduce and investigate a new notion of dimension for continuous mappings between topological spaces, which is closer to the classical definition of the Lebesgue covering dimension of a space. We discuss various results concerning this dimen-sion. Moreover, we present open questions and proposals of new dimensions of continuous mappings for further studies. They are based on known dimensions of continuous mappings between topological spaces.
relationships between the dimensions of the domain and range of a continuous mapping. Most of the theorems deal with mappings that satisfy additional conditions such as being closed mappings. In the “environment” of such studies, dimensions of continuous mappings have been also studied. In this paper, we introduce and investigate a new notion of dimension for continuous mappings between topological spaces, which is closer to the classical definition of the Lebesgue covering dimension of a space. We discuss various results concerning this dimen-sion. Moreover, we present open questions and proposals of new dimensions of continuous mappings for further studies. They are based on known dimensions of continuous mappings between topological spaces.