Continuous Selections. I

Overview.- An Overview of Empirical Processes.- Overview of Semiparametric Inference.- Case Studies I.- Empirical Processes.- to Empirical Processes.- Preliminaries for Empirical Processes.- Stochastic Convergence.- Empirical Process Methods.- Entropy Calculations.- Bootstrapping Empirical Processes.- Additional Empirical Process Results.- The Functional Delta Method.- Z-Estimators.- M-Estimators.- Case Studies II.- Semiparametric Inference.- to Semiparametric Inference.- Preliminaries for Semiparametric Inference.- Semiparametric Models and Efficiency.- Efficient Inference for Finite-Dimensional Parameters.- Efficient Inference for Infinite-Dimensional Parameters.- Semiparametric M-Estimation.- Case Studies III.

Introduction to empirical processes and semiparametric inference

Infinite dimensional analysis

Multicomponent reactions in organic-chemistry

Publisher Summary This chapter discusses generalized metric spaces. Any class of spaces defined by a property possessed by all metric spaces could be called a class of generalized metric spaces. The term is meant for classes that are close to metrizable spaces in some sense. They usually possess some of the useful properties of metric spaces, and some of the theory or techniques of metric spaces carries over to these wider classes. They can be used to characterize the images or pre-images of metric spaces under certain kinds of mappings. They often appear in theorems that characterize metrizability in terms of weaker topological properties. They should be stable under certain topological operations, such as finite or countable products, closed subspaces, and perfect mappings. This class has played an important role in the dimension theory of general spaces. The theory of generalized metric spaces is closely related to what is known as metrization theory.

Generalized Metric Spaces

Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

Fixed Point Theory

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An extension of Tietze's theorem.

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Topologies for function spaces

The presently available chemical computer programs are discussed, as well as the fact that a mathematical theory of constitutional chemistry is needed as a basis for substantial progress in computer assisted solutions to chemical problems. The representation of EM 1) and their interconversions by be-matrices 1) and reaction matrices leads to the logical structure of the FIEM 1) and is representative for constitutional chemistry. A mathematical theory of the FIEM is stated, which can serve as the foundation of a new type of matrix-fitting computer programs for establishing constitutional relations such as synthetic design, the elucidation of reaction mechanisms, and bio-synthetic pathways, as well as the analysis of mass spectra.

James Dugundji

Papers

Fixed Point Theory

An extension of Tietze's theorem.

Topologies for function spaces

An algebraic model of constitutional chemistry as a basis for chemical computer programs

Remark on the concept of compactness