Infinite games and chain conditions

Santi Spadaro

Fundamenta Mathematicae (2016)

  • Volume: 234, Issue: 3, page 229-239
  • ISSN: 0016-2736

Abstract

top
We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the G δ topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak Lindelöf property, every cover by G δ sets has a continuum-sized subcollection whose union is G δ -dense.

How to cite

top

Santi Spadaro. "Infinite games and chain conditions." Fundamenta Mathematicae 234.3 (2016): 229-239. <http://eudml.org/doc/286469>.

@article{SantiSpadaro2016,
abstract = {We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the $G_\{δ\}$ topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak Lindelöf property, every cover by $G_\{δ\}$ sets has a continuum-sized subcollection whose union is $G_\{δ\}$-dense.},
author = {Santi Spadaro},
journal = {Fundamenta Mathematicae},
keywords = {chain conditions; selectively ccc; selection principles; weakly lindel"of; topological games; cardinal inequality},
language = {eng},
number = {3},
pages = {229-239},
title = {Infinite games and chain conditions},
url = {http://eudml.org/doc/286469},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Santi Spadaro
TI - Infinite games and chain conditions
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 3
SP - 229
EP - 239
AB - We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the $G_{δ}$ topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak Lindelöf property, every cover by $G_{δ}$ sets has a continuum-sized subcollection whose union is $G_{δ}$-dense.
LA - eng
KW - chain conditions; selectively ccc; selection principles; weakly lindel"of; topological games; cardinal inequality
UR - http://eudml.org/doc/286469
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.