Title of article :
Characters of countably tight spaces and inaccessible cardinals
Usuba، نويسنده , , Toshimichi، نويسنده ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2014
In this paper, we study some connections between characters of countably tight spaces of size ω 1 and inaccessible cardinals. A countable tight space is indestructible if every σ-closed forcing notion preserves countable tightness of the space. We show that, assuming the existence of an inaccessible cardinal, the following statements are consistent:(1)
indestructibly countably tight space of size ω 1 has character ⩽ ω 1 .
> ω 2 and there is no countably tight space of size ω 1 and character ω 2 .
he converse, we show that, if ω 2 is not inaccessible in the constructible universe L, then there is an indestructibly countably tight space of size ω 1 and character ω 2 .
Countable tight space , Countable tightness indestructibility , Topological game , Kurepa tree , Inaccessible cardinal
Journal title :
Topology and its Applications