| CHAPTER I | PRELIMINARIES | §1 General facts
§2 Topological spaces and maps
§3 Metric spaces and complete metric spaces
§4 Operations on topological spaces
§5 Spaces of maps. Homotopies and isotopies
§6 Linear spaces and convex sets. Linear topological spaces
§7 Banach spaces and normed linear spaces |
| CHAPTER II | TOPOLOGICAL SPACES WITH CONVEX
STRUCTURES | §1 Isometric embeddings of metric spaces into function spaces
§2 Covers, partitions of unity, paracompactness
§3 The Dugundji extension formula and its applications
§4 Local properties
§5 ANE's and ANR's
§6 Simplicial complexes and topological spaces dominated by simplicial complex spaces
§7 Michael's theory of continuous selections |
| CHAPTER III | CONVEX SETS AND DELETING
HOMEOMORPHISMS IN LINEAR TOPOLOGICAL SPACES | §1 Preliminaries
§2 Affine embeddings of locally compact closed sets into Banach spaces
§3 Keller spaces. The theorem of Keller
§4 Topological homogeneity of the Hilbert cube
§5 Non-complete-norm technique of deleting sets
§6 Relative topological classification of closed convex bodies in a linear topological space
§7 Topological classification of locally compact closed convex sets in Banach spaces
§8 Notes |
| CHAPTER IV | SKELETONS AND SKELETOIDS IN METRIC
SPACES | §1The group Auth X
§2 Equivalence of skeletoids
§3 Estimated extensions of K-embeddings. Perfect collections
§4 Skeletons related to perfect collections. The theorem of Toruńczyk
§5 Strongly negligible sets
§6 Pseudotranslations. The product scheme of extending homeomorphisms
§7 Perfect collections of finite sets. Applications to manifolds
§8 Theorem of Fort
§9 Notes |
| CHAPTER V | Z-SETS IN THE HILBERT CUBE AND IN
THE COUNTABLE INFINITE PRODUCT OF LINES | §1 Preliminaries
§2 Anderson's Z-sets in the Hilbert cube
§3 Z-skeletoids in Q
§4 Z-skeletoids in Keller spaces
§5 EZ-skeletoids in Keller spaces
§6 Z-sets in the countable infinite product of lines
§7 The Brown-Gluck stability
§8 Notes |
| CHAPTER VI | SPACES HOMEOMORPHIC TO THE
COUNTABLE INFINITE PRODUCT OF LINES | §1 The topological apparatus
§2 An application to the Hilbert space l2
§3 Kadeo's renorming theorems for separable Banach spaces
§4 Fréchet spaces with a quotient space isomorphic to R�
§5 The homeomorphism of all infinite-dimensional separable Fréchet spaces
§6 Topological classification of convex bodies in Fréchet spaces
§7 Spaces of measurable functions
§8 Miscellaneous theorems adn examples
§9 Kadec's proof of the homeomorphism of all infinite-dimensional separable Banach spaces
§10 Notes and historical remarks |
| CHAPTER VII | TOPOLOGICAL CLASSIFICATION OF
NON-SEPARABLE FRÉCHET SPACES | §1 The decomposition scheme
§2 The decomposition criterion
§3 Transfinite projection bases
§4 Topological classification of reflexive Banach spaces
§5 The theorem of Troyanski
§6 Homeomorphism of spaces of bounded linear operators and product spaces
§7 Homeomorphism of non-separable function spaces
§8 Notes |
| CHAPTER VIII | TOPOLOGICAL CLASSIFICATION OF
NON-SEPARABLE LINEAR METRIC SPACES | §1 Absolute Borelian classes and projective classes of metric spaces
§2 Borelian and projective classification of linear metric spaces. Existence theorems of Mazur and Klee
§3 Linear metric spaces representable as E-skeletoids and EE-skeletoids in the countable infinite product of lines
§4 Applications to certain product spaces
§5 Toplogical classification of sigma-compact normed linear spaces
§6 Notes |
| CHAPTER IX | INFINITE-DIMENSIONAL TOPOLOGICAL
MANIFOLDS | §1 Topological manifolds; atlases, closed embeddings
§2 Spaces with reflective isotopy property. Wong's deformation
§3 Maps into reduced Cartesian products. Theorem of West on fixed-point sets of transformation groups
§4 The stability theorem of Anderson and Schori
§5 Starlike spaces and conical spaces
§6 Infinite-dimensional microbundles
§7 Infinite-dimensional manifolds: open embedding theorem, topological classification by homotopy type
§8 Notes |
Prosimy o przesyłanie uwag na adres bwm@icm.edu.pl