2. SELECTION PRINCIPLES IN TOPOLOGY Doctoral dissertation by Liljana Babinkostova

3. HISTORY 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

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

5. Standard themes

15. Examples:

20. General Implications

23. Star selection principles

28. X is a Tychonoff space Y is a subspace of X f is a continuous function Assumptions

29. The sequence selection property

30. Countable fan tightness

31. Countable strong fan tightness

32. Strongly Frechet function

33. (X,d) is a metric space Y is a subspace of X Y is a subspace of X Assumptions:

34. Relative Menger basis property

35. Relative Hurewicz basis property

36. Relative Scheepers basis property

37. Relative Rothberger basis property

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

39. Relative Menger measure zero

40. Relative Hurewicz measure zero

41. Relative Scheepers measure zero

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