Feebly compact implies pseudocompact

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This article gives the statement and possibly, proof, of an implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., feebly compact space) must also satisfy the second topological space property (i.e., pseudocompact space)
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Statement

Any feebly compact space is a pseudocompact space.

Facts used

  1. Feeble compactness is continuous image-closed
  2. Compact iff feebly compact for subsets of Euclidean space