Cardinality of Compact Hausdorff Space and Kurepa Tree
[TMCSC]
August 04, 2020 20:30-21:30
腾讯会议（线上）
SPEAKER
金人麟（美国查理斯顿学院）
ABSTRACT
A second countable compact Hausdorff space X must have cardinality either aleph 0 or two to the aleph 0 power. If a non-second countable compact Hausdorff space Y has a topological base with cardinality aleph 1, then we cannot conclude that the cardinality of Y must be either aleph 1 or two to the aleph 1 power when two to the aleph 1 power is strictly greater than aleph 2. The question which set S of cardinals strictly between aleph 1 and two to the aleph 1 power including empty set could be the cardinalities of all these Y's is independent of ZFC plus Continuum Hypothesis. The question when S is an empty set is even related to the existence of an inaccessible cardinal. We will translate the question to the question about aleph 1 trees and analyze the question by studying these trees. The trees are similar but different from well-known Kurepa trees. We will mention a recent result of Poor and Shelah on this study near the end of the talk.
ORGANIZERS
黄南京（四川大学）
寇 辉（四川大学）
连 增（四川大学）
张德学（四川大学）
张伟年（四川大学）
SUPPORTED BY
国家天元数学西南中心
四川大学数学学院
VIDEO
- Cardinality of Compact Hausdorff Space and Kurepa Tree
- 20:30 - 21:30, 2020-08-04 at 腾讯会议（线上）
- 金人麟（美国查理斯顿学院）