Topologies Generated by Discrete Subspaces
نویسندگان
چکیده
A topological space X is called discretely generated if for every subset A⊂X we have A=∪{D:D⊂A and D is a discrete subspace of X}. We say that X is weakly discretely generated if A⊂X and A6=A implies D\A6=∅ for some discrete D⊂A. It is established that sequential spaces, monotonically normal spaces and compact countably tight spaces are discretely generated. We also prove that every compact space is weakly discretely generated and under the Continuum Hypothesis any dyadic discretely generated space is metrizable.
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