Editing Topologist's sine curve (section)

==Properties==

The topologist's sine curve {{mvar|T}} is [[connected space|connected]] but neither [[locally connected space|locally connected]] nor [[connected space#Path connectedness|path connected]]. This is because it includes the point {{math|(0, 0)}} but there is no way to link the function to the origin so as to make a [[path (topology)|path]].

The space {{mvar|T}} is the continuous image of a [[locally compact]] space (namely, let {{mvar|V}} be the space <math>\{-1\} \cup (0, 1],</math> and use the map <math>f : V \to T</math> defined by <math>f(-1) = (0,0)</math> and <math>f(x) = (x, \sin\tfrac{1}{x})</math> for {{math|''x'' > 0}}), but {{mvar|T}} is not locally compact itself.

The [[topological dimension]] of {{mvar|T}} is 1.