Starts at: 2025-03-08 10:20AM
Ends at: 2025-03-08 10:40AM
Abstract:
Suppose that a topological space $X$ has no uncountable discrete subspace. We discuss if $X$ can obtain an uncountable discrete subspace in forcing extensions. We prove that for any monotonically normal space $X$ which has no uncountable discrete subspace, $X$ can obtain an uncountable discrete subspace in some forcing extension if and only if $X$ is not separable.