Supercompact Spaces

  title={Supercompact Spaces},
  author={Eric van DOUWEN and Jan van Mill},
We prove the following theorem: Let Y be a Hausdorff space which is the continuous image of a supercompaet Hausdorff space, and let K be a countably infinite subset of Y. Then (a) at least one cluster point of K is the limit of a nontrivial convergent sequence in Y (not necessarily in K), and (b) at most countably many cluster points of K are not the limit of some nontrivial sequence in Y. This theorem implies that spaces like (3N and (3N\N are not supercompact. Moreover we will give an example… CONTINUE READING

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