Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Local path-connectedness v. path-connectedness

  1. May 12, 2008 #1
    Can a space be path-connected and not locally path-connected? (To be clear, "locally path-connected" just means that there is a basis of path-connected of sets.)

    My general intuition says no, but my intuition seems to usually be wrong...and this would explain why Hatcher keeps referring to spaces that are both p.c. and l.p.c. in his Algebraic Topology....
     
  2. jcsd
  3. May 12, 2008 #2
    My first time around google didn't bring me to this site which claims to contradict my intuition. So I guess this thread can be ignored...
     
  4. May 12, 2008 #3

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    what is the definition of lcp?
     
  5. May 12, 2008 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    well planet maths ays lcp means every nbhd of p conrtains a pc nbhd.

    so just take any silly space like say the union of the y axis, the x axis and the horizontal lines at ordinates y = 1/n.

    thAT SHOULD BE PATH CONNECTED AND NOT LOCALLY SO at any point of the x axis except (0,0).
     
  6. May 12, 2008 #5
    That's a pretty nice example of such a space.

    Well I guess it's time to fine-tune my intuition....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Local path-connectedness v. path-connectedness
  1. Connectedness problem (Replies: 10)

  2. Parametrizing Paths (Replies: 3)

  3. Definition of path (Replies: 3)

  4. Path independence (Replies: 1)

Loading...