A study of the existence of equilibrium in mathematical economics
- Authors: Xotyeni, Zukisa Gqabi
- Date: 2008
- Subjects: Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5418 , http://hdl.handle.net/10962/d1005232 , Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Description: In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.
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Lattice-valued uniform convergence spaces the case of enriched lattices
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
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