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54D05 - General topology :: Fairly general properties :: Connected and locally connected spaces

  1. \mathbb{R}^2 \setminus C is path connected if C is countable owned by silverfish
  2. a connected and locally path connected space is path connected owned by Mathprof
  3. a connected normal space with more than one point is uncountable owned by azdbacks4234
  4. balls in ultrametric spaces are clopen subsets owned by MFH
  5. clopen subset owned by mathcam
  6. completely separated owned by CWoo
  7. connected component owned by djao
  8. connected im kleinen owned by Mathprof
  9. connected set in a topological space owned by ack
  10. connected space owned by mathcam
  11. connectedness is preserved under a continuous map owned by drini
  12. continuous images of path connected spaces are path connected owned by mps
  13. cut-point owned by mathcam
  14. example of a connected space that is not path-connected owned by yark
  15. example of a semilocally simply connected space which is not locally simply connected owned by antonio
  16. example of a space that is not semilocally simply connected owned by mathcam
  17. generalized Hurewicz fundamental theorem owned by bci1
  18. generalized Hurewicz fundamental theorem owned by bci1
  19. homeomorphisms preserve connected components owned by joking
  20. hyperconnected space owned by yark
  21. intervals are connected owned by joking
  22. Jordan curve theorem owned by rmilson
  23. limit points and closure for connected sets owned by matte
  24. locally connected owned by djao
  25. locally simply connected owned by Dr_Absentius
  26. path owned by rspuzio
  27. path component owned by djao
  28. product of path connected spaces is path connected owned by joking
  29. products of connected spaces are connected owned by mps
  30. proof that a path connected space is connected owned by n3o
  31. proof that products of connected spaces are connected owned by yark
  32. quasicomponent owned by Evandar
  33. semilocally simply connected owned by djao
  34. separated owned by matte
  35. ultraconnected space owned by yark
  36. union of non-disjoint connected sets is connected owned by matte
  37. when are balls separated owned by matte

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