Rudin is best known in topology for her constructions of counterexamples to well-known conjectures. In 1958, she found an unshellable triangulation of the tetrahedron. Most famously, Rudin was the first to construct a Dowker space, which she did in 1971, thus disproving a conjecture of Clifford Hugh Dowker that had stood, and helped drive topological research, for more than twenty years. Her example fueled the search for "small" ZFC Dowker spaces. She also proved the first Morita conjecture and a restricted version of the second. Her last major result was a proof of Nikiel's conjecture. Early proofs that every metric space is paracompact were somewhat involved, but Rudin provided an elementary one.
