SELECTION PRINCIPLES IN TOPOLOGY

1. SELECTION PRINCIPLES IN TOPOLOGY Doctoral dissertation by Liljana Babinkostova

2. 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

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

4. Standard themes

5. Selection principle

6. Selection principle

7. Selection principle

8. C-property

9. Screenability

10. NEW selection principle

12. RELATIONS

13. RELATIONS

14. RELATIONS Examples:

16. Relative selection principles

17. Relative selection principles

18. Relative star-selection principles

19. Equivalences and implications General Implications

20. Equivalences and implications

21. Equivalences and implications

22. Equivalences and implications Star selection principles

24. Topological operations

25. Topological operations

26. Game theory

27. Assumptions Duality theory • X is a Tychonoff space • Y is a subspace of X • f is a continuous function

28. The sequence selection property

29. Countable fan tightness

30. Countable strong fan tightness

31. Strongly Frechet function

32. (X,d) is a metric space Y is a subspace of X Basis properties Assumptions:

33. Relative Menger basis property

34. Relative Hurewicz basis property

35. Relative Scheepers basis property

36. Relative Rothberger basis property

37. Measure properties Assumptions: (X,d) is a zerodimensional metric space Y is a subspace of X

38. Relative Menger measure zero

39. Relative Hurewicz measure zero

40. Relative Scheepers measure zero

41. http://iunona.pmf.ukim.edu.mk/~spm S P M