SELECTION PRINCIPLES IN TOPOLOGY

1 / 41

# SELECTION PRINCIPLES IN TOPOLOGY - PowerPoint PPT Presentation

SELECTION PRINCIPLES IN TOPOLOGY. Doctoral dissertation by Liljana Babinkostova. E. Borel 1919 Strong Measure Zero metric spaces K. Menger 1924 Sequential property of bases of metric spaces W. Hurewicz 1925 F.P. Ramsey 1930 Ramsey's Theorem

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'SELECTION PRINCIPLES IN TOPOLOGY' - teenie

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### SELECTION PRINCIPLES IN TOPOLOGY

Doctoral dissertation by

Liljana Babinkostova

E. Borel 1919 Strong Measure Zero metric spaces

K. Menger 1924 Sequential property of bases of metric spaces

W. Hurewicz 1925

F.P. Ramsey 1930 Ramsey's Theorem

F. Rothberger 1938

R.H.Bing 1951 Screenability

HISTORY
HISTORY
• F. Galvin 1971
• R. Telgarsky 1975
• J. Pawlikovski 1994 ,
• Lj.Kocinac 1998 Star-selection principles
• M.Scheepers 2000 Groupability

RELATIONS

Examples:

Equivalences and implications

General Implications

Equivalences and implications

Star selection principles

Assumptions

Duality theory

• X is a Tychonoff space
• Y is a subspace of X
• f is a continuous function
(X,d) is a metric space

Y is a subspace of X

Basis properties

Assumptions:

Measure properties

Assumptions:

(X,d) is a zerodimensional metric space

Y is a subspace of X