Heath’s V-space is just the upper half-plane, with an unusual topology, in which all points above the x-axis are open, and the basic open neighborhoods of a point (x, 0) on the x-axis are ... the various symmetric “open V ”s, with 45-degree fingers of arbitrary equal non-zero lengths, as shown.

  (These are just the images of the vertical symmetric basic open neighborhoods of (x, 0) in R_discrete × R_metric under the quotient map (x, y) ·-·-·> (x+y, |y|) .)

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