TY - JOUR

T1 - Some observations on a clopen version of the Rothberger property

AU - Bhardwaj, Manoj

AU - Osipov, Alexander v.

PY - 2023

Y1 - 2023

N2 - In this paper, we prove that a clopen version S1(CO, CO) of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space (X, d), X satisfies S1(CO, CO) if, and only if, X has Borel strong measure zero with respect to each metric which has the same topology as d has. In a zero-dimensional space, the game G1(O, O) is equivalent to the game G1(CO, CO) and the point-open game is equivalent to the point-clop en game. Using reflections, we obtain that the game G1(CO, CO) and the point-clop en game are strategically and Markov dual. An example is given for a space on which the game G1(CO, CO) is undetermined.

AB - In this paper, we prove that a clopen version S1(CO, CO) of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space (X, d), X satisfies S1(CO, CO) if, and only if, X has Borel strong measure zero with respect to each metric which has the same topology as d has. In a zero-dimensional space, the game G1(O, O) is equivalent to the game G1(CO, CO) and the point-open game is equivalent to the point-clop en game. Using reflections, we obtain that the game G1(CO, CO) and the point-clop en game are strategically and Markov dual. An example is given for a space on which the game G1(CO, CO) is undetermined.

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001068779900001

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85176922721

U2 - 10.56754/0719-0646.2502.161

DO - 10.56754/0719-0646.2502.161

M3 - Article

VL - 25

SP - 161

EP - 172

JO - Cubo

JF - Cubo

SN - 0716-7776

IS - 2

ER -