Selection theory for infinite dimensional spaces and continuous single-valued approximations to upper semi-continuous multivalued mappings

<p>The extension problem is one of the fundamental problems of topology; if TX and Y are topological spaces and A is a closed subset of X and f:A —> Y is a continuous function, under what conditions is there »a continuous function fzx + Y such‘ that fIA = f ? Two key theorems of topology deal with this problem. They are the Tietze Extension A Theorem and the Brouwer No—Retraction Theorem. The first states that 1‘:-X is a normal Hausdorff space and Y is the real line then any continuous function f from a closed subset A of X into Y can be extended to a continuous function from X into Y . The second states that if X is the (n +1) -ball and Y and A are both the n-sphere bounding X in En+1 then the identity mapping from A to Y cannot be extended to a continuous function from X to Y.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematical Sciences

Year

1972

Author dc:creator

• Pixley, Carl Preston

Contributors dc:contributor

• Prabir Roy
• Louis F. McAuley
• Harry W. Berkowitz

• Topological spaces
• Topology
• Selection theory
• Infinite dimensional spaces
• Continuous single-valued approximations
• Semi-continuous multivalued mappings

Repository record dc:identifier

https://orb.binghamton.edu/dissertation_and_theses/181

OAI identifier oai:identifier

oai:orb.binghamton.edu:dissertation_and_theses-1187