Titlebook: Geometric Aspects of General Topology; Katsuro Sakai Book 2013 Springer Japan 2013

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1439-7382 strated by figures or diagrams for easier understanding.Fasc.This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology a

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Elisavet M. Sofikitou,Markos V. Koutrasics of paracompact spaces that indicate, in many situations, the advantages of paracompactness. In particular, there exists a useful theorem showing that, if a paracompact space has a certain property ., then it has the same property .. Furthermore, paracompact spaces have partitions of unity, which is also a very useful property.

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https://doi.org/10.1007/978-3-322-93105-4ct (surjective) map . : . → . such that each fiber ..(.) is cell-like. The concept of cell-like maps is very important in Geometric Topology. It has been mainly developed in Shape Theory and Decomposition Theory. For infinite-dimensional manifolds (in particular Hilbert cube manifolds), this concept is one of the main tools.

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Metrization and Paracompact Spaces, perfect maps. Several metrization theorems are proved, and we characterize completely metrizable spaces. We will study several different characteristics of paracompact spaces that indicate, in many situations, the advantages of paracompactness. In particular, there exists a useful theorem showing t

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Topology of Linear Spaces and Convex Sets,bility, and normability of topological linear spaces. Among the important results are the Hahn–Banach Extension Theorem, the Separation Theorem, the Closed Graph Theorem, and the Open Mapping Theorem. We will also prove the Michael Selection Theorem, which will be applied in the proof of the Bartle–

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Dimensions of Spaces,ch . open cover of . has a . open refinement . with .. and then, dim. = . if dim. ≤ . and dim. ≮ .. By ., we mean that . = .. We say that . is .-. if dim. = . and that . is . (.) (dim. < .) if dim. ≤ . for some . ∈ .. Otherwise, . is said to be . (.) (dim. = .). The dimension is a topological invari