The story
The H was suggested by Jean-Pierre Serre in recognition of the influence exerted on the subject by Heinz Hopf.
Etymology from Wiktionary, CC BY-SA 4.0.
H-space
Today it means: A topological space X (generally assumed to be connected) together with a continuous map μ : X × X → X with an identity element e such that μ(e, x) = μ(x, e) = x for all x in X. Full definition →