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  1. Path: sparky!uunet!olivea!spool.mu.edu!agate!doc.ic.ac.uk!mrccrc!warwick!pipex!pavo.csi.cam.ac.uk!emu.pmms.cam.ac.uk!rgep
  2. From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
  3. Newsgroups: sci.math
  4. Subject: Re: definition of topological space
  5. Summary: Definition of continuity in terms of closed sets works just as well
  6. Keywords: Topology; Open sets; Continuity; Closed sets
  7. Message-ID: <1992Nov6.101258.3345@infodev.cam.ac.uk>
  8. Date: 6 Nov 92 10:12:58 GMT
  9. References: <1992Nov5.033835.5180@leland.Stanford.EDU> <1992Nov5.094404.15550@infodev.cam.ac.uk> <1992Nov6.092037.7676@leland.Stanford.EDU>
  10. Sender: news@infodev.cam.ac.uk (USENET news)
  11. Organization: Department of Pure Mathematics, University of Cambridge
  12. Lines: 14
  13. Nntp-Posting-Host: emu.pmms.cam.ac.uk
  14.  
  15. In article <1992Nov6.092037.7676@leland.Stanford.EDU> ledwards@leland.Stanford.EDU (Laurence James Edwards) writes:
  16. >[...]
  17. >In defining continuity what is the advantage of using open sets vs. closed sets,
  18. >i.e. why not say:
  19. >
  20. > |x-x'| <= e => |f(x) - f(x')| <= d
  21. >
  22. >and similarly:
  23. >
  24. > Y closed => f*(Y) closed
  25. >
  26. No reason, except maybe historical.  It works just as well.
  27.  
  28. Richard Pinch
  29.