SELECTION PRINCIPLES IN TOPOLOGY
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Transcript of SELECTION PRINCIPLES IN TOPOLOGY
SELECTION PRINCIPLES IN SELECTION PRINCIPLES IN TOPOLOGYTOPOLOGY
Doctoral dissertation by
Liljana BabinkostovaLiljana Babinkostova
HISTORYHISTORY 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
HISTORYHISTORY
F. Galvin 1971
R. Telgarsky 1975
J. Pawlikovski 1994 ,
Lj.Kocinac 1998 Star-selection principles
M.Scheepers 2000 Groupability
Standard themes
O O O O
1: BASIC DIAGRAM FOR Sc-PROPERTY
Examples:Examples:
2:THES1¡Sc-DIAGRAM
: THE S1 - Sc DIAGRAM
General ImplicationsGeneral Implications
Star selection principlesStar selection principles
• X is a Tychonoff space
• Y is a subspace of X
• f is a continuous function
Assumptions
The sequence selection property
Countable fan tightnessCountable fan tightness
Countable strong fan tightness
Strongly Frechet function
(X,d) is a metric space Y is a subspace of XY is a subspace of X
Assumptions:
Relative Menger basis propertyRelative Menger basis property
Relative Hurewicz basis property
PartitionRelations
Relative Scheepers basis property
Relative Rothberger basis property
(X,d) is a zerodimensional metric space Y is a subspace of XY is a subspace of X
Assumptions:
Relative Menger measure zero
Relative Hurewicz measure zero
Relative Scheepers measure zero
http://iunona.pmf.ukim.edu.mk/~spmhttp://iunona.pmf.ukim.edu.mk/~spm
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