TOPICS
Search

Normed Space


A normed space, also called a normed linear space, is a vector space possessing a norm.

The Petty equilateral-set conjecture asks whether every real d-dimensional normed space contains d+1 pairwise equidistant points. Yang (2026) reported the five-dimensional case, with a proof generated by Tencent Hunyuan hyprover and checked by the author. That argument requires independent specialist assessment.


See also

Bounded Operator, Jung Constant, Minkowski Plane, Norm, Normed Ring, Projection Constant, Vector Space

Explore with Wolfram|Alpha

References

Yang, K. "Petty's Equilateral-Set Conjecture in Dimension Five." 29 Oct 2026. https://arxiv.org/abs/2610.39967.

Referenced on Wolfram|Alpha

Normed Space

Cite this as:

Weisstein, Eric W. "Normed Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NormedSpace.html

Subject classifications