Topologist's Sine Curve

  9
T0 1
T1 1
Hausdorff 1
T3 •
T4 •
T5 •
Completely Hausdorff •
T3.5 •
Urysohn •
Semiregular •
Perfectly Normal •
Separable •
Second Countable •
First Countable •
Lindelof •
Compact •
Sigma-Compact •
Countably Compact •
Sequentially Compact •
Limit Point Compact •
Pseudocompact •
Locally Compact •
Strongly Locally Compact •
Connected 1
Path Connected 0
Arc Connected •
Locally Connected •
Locally Path Connected •
Metrizable •
Totally Pathwise Disconnected •
Totally Disconnected •
Totally Separated •

Description: The graph of $\sin(1/x)$ over the interval $(0,1]$ extended by the single point $(0,0)$ (with topology induced from the Euclidean plane).

Human-entered properties: Computer-inferred properties: Deleted properties: (none)

Sometimes you'll see a check properties link on the left column of this page. If you see it then it means the computer has not checked the human entered properties. The check properties link invokes the logical inference engine to determine if there are any properties which can be determined automatically.