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54D30 - General topology :: Fairly general properties :: Compactness

  1. Y is compact if and only if every open cover of Y has a finite subcover owned by mathcam
  2. a compact set in a Hausdorff space is closed owned by mathcam
  3. a space is compact iff any family of closed sets having fip has non-empty intersection owned by CWoo
  4. alternative characterization of Stone-Čech compactification owned by rspuzio
  5. closed set in a compact space is compact owned by mathcam
  6. closed subsets of a compact set are compact owned by Wkbj79
  7. compact owned by djao
  8. compact subspace of a Hausdorff space is closed owned by ehremo
  9. compactness is preserved under a continuous map owned by yark
  10. continuous image of a compact set is compact owned by Wkbj79
  11. examples of compact spaces owned by yark
  12. finite intersection property owned by azdbacks4234
  13. Heine-Borel theorem owned by Evandar
  14. point and a compact set in a Hausdorff space have disjoint open neighborhoods. owned by drini
  15. proof of Heine-Borel theorem owned by stevecheng
  16. proof of Tychonoff's theorem owned by asteroid
  17. proof of Tychonoff's theorem in finite case owned by stevecheng
  18. proof that a compact set in a Hausdorff space is closed owned by yark
  19. proof that a metric space is compact if and only if it is complete and totally bounded owned by rm50
  20. properties of compact spaces owned by rspuzio
  21. pseudocompact space owned by yark
  22. relationship among different kinds of compactness owned by rm50
  23. representation theorem for compact metric spaces owned by matte
  24. sequentially compact owned by mps
  25. Stone-Čech compactification owned by rspuzio
  26. the continuous image of a compact space is compact owned by cvalente
  27. The property that compact sets in a space are closed lies strictly between T1 and T2 owned by dfeuer
  28. topological condition for a set to be uncountable owned by mps
  29. tube lemma owned by asteroid
  30. Tychonoff's theorem owned by matte
  31. Tychonoff's theorem implies AC owned by CWoo
  32. weakly countably compact owned by yark

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