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Developing a dimension theory: on the basis of almost zerodimensionality,Used
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This is nearly a century that dimension theory plays a crucial role in topology. Almost zerodimensionality as a dimension theoretic concept that fits neatly between zero and onedimensionality introduced in 1994 and the famous Erdos space is a universal object in the class of all almost zerodimensional spaces. The main aim of this book is to find the right way to extend almostzero dimensionality, that is, to develop a dimension theory on the basis of this notion. We introduce the notion of an almost ndimensional space. In this way an important result is a topological analogue of the classic Kadec Renorming Theorem for Banach spaces which produces an elegant topological characterization of our new concept. Construction of higher dimensional analogues of complete Erdos space that are universal spaces for almost ndimensionality is another interesting result. This book may be readable and useful for anyone interested to mathematical analysis or general topology.
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