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SELECTION PRINCIPLES IN TOPOLOGY. Doctoral dissertation by Liljana Babinkostova. 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

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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 Ramsey's Theorem

F. Rothberger 1938

R.H.Bing 1951 Screenability

HISTORY
history3
HISTORY
  • F. Galvin 1971
  • R. Telgarsky 1975
  • J. Pawlikovski 1994 ,
  • Lj.Kocinac 1998 Star-selection principles
  • M.Scheepers 2000 Groupability
slide14

RELATIONS

Examples:

slide19

Equivalences and implications

General Implications

slide22

Equivalences and implications

Star selection principles

assumptions
Assumptions

Duality theory

  • X is a Tychonoff space
  • Y is a subspace of X
  • f is a continuous function
x d is a metric space y is a subspace of x
(X,d) is a metric space

Y is a subspace of X

Basis properties

Assumptions:

slide37

Measure properties

Assumptions:

(X,d) is a zerodimensional metric space

Y is a subspace of X