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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