NMSU • BLAST-2009
Something Old, Something New, Something Borrowed, ...
Next F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus

One open V nbhd   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 Rdiscrete × Rmetric under the quotient map (x, y) ·-·-·> (x+y, |y|) .)

  Notation: Vε(x) = {(x+r, |r|) : 0 < |r| < ε} (ε > 0, x ∈ R).

  As for two such neighborhoods at distinct points, Vε(x) and Vε'(y) ,