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SELECTION PRINCIPLES IN TOPOLOGY Doctoral dissertation by Liljana Babinkostova 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 F. Rothberger 1938 R.H.Bing 1951 Ramsey's Theorem Screenability HISTORY F. Galvin 1971 R. Telgarsky 1975 J. Pawlikovski 1994 Lj.Kocinac 1998 Star-selection principles M.Scheepers 2000 Groupability , Standard themes 1: BASIC DIAGRAM FOR Sc-PROPERTY Examples: : T HE S1 - Sc DI AGRA M General Implications Star selection principles Assumptions • X is a Tychonoff space • Y is a subspace of X • f is a continuous function The sequence selection property Countable fan tightness Countable strong fan tightness Strongly Frechet function Assumptions: (X,d) is a metric space Y is a subspace of X Relative Menger basis property Relative Hurewicz basis property Relative Scheepers basis property Relative Rothberger basis property Assumptions: (X,d) is a zerodimensional metric space Y is a subspace of X Relative Menger measure zero Relative Hurewicz measure zero Relative Scheepers measure zero S P M http://iunona.pmf.ukim.edu.mk/~spm