Download SELECTION PRINCIPLES IN TOPOLOGY

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