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| ``Topologist's sine curve is connected.''
by jrottman on 2008-04-02 23:31:10 |
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| | I'm having trouble grasping that the topologist's sine curve is connected. I think where I'm stuck is, "... any open set which contains points of the line segment X1 must contain points of X2." Isn't, for example, (0, (-.5, .5)) an open subset of X1? Does an open set containing a point of X1 have to cover intervals in both the x-dimension and y-dimension? Is that what is meant by, "the topology induced from R2?" |
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