by Kenneth Kunen and Arnold Miller
There is an excellent biographical interview of Mary Ellen published
in
[e2].
Also, there is an entire volume
[e3]
devoted to articles
describing her mathematics. All quotations below are taken from
[e3].
Mary Ellen Rudin was one of the leading topologists of our time.
Besides solving a number of well-known outstanding open problems, she
was a pioneer in the use of set-theoretic tools. She was one of the
first to apply the independence methods of Cohen and others to produce
independence results in topology. She did not do forcing arguments
herself, but many of her papers make use of set-theoretic statements,
such as Martin’s Axiom, Suslin’s Hypothesis, and
In her thesis [1] she gave an example of a nonseparable Moore space that satisfies the countable chain condition. She published the results of her thesis in three papers in the Duke Math Journal [2], [3], [4]. To quote Steve Watson, “This cycle represents one of the greatest accomplishments in set-theoretic topology. However the mathematics in these papers is of such depth that, even forty years later, they remain impenetrable to all but the most diligent and patient of readers.”
![](https://celebratio.org/media/cunit/None_cunit_lecturing.jpg)
In
[5]
she used a Suslin tree to construct a Dowker space. The
existence of a Suslin tree is consistent with ZFC but not provable
from ZFC. In
[6]
[8] she constructed a Dowker space just in ZFC.
This space has cardinality
Mary Ellen is famous for her work on box products. If
Mary Ellen is also famous for her work on
The Rudin–Frolik order led to the first proof in ZFC that the space of
nonprincipal ultrafilters,
For the Rudin–Frolik order, for
![](https://celebratio.org/media/cunit/None_cunit_kunenfest.jpg)
The Rudin–Keisler order comes naturally out of the notion of induced
measure. If
In 1999, almost a decade after her retirement, Mary Ellen settled a long-standing conjecture in set-theoretic topology by showing that every monotonically normal compact space is the continuous image of a linearly ordered compact space. This paper [15] was the final one in a series of five which gradually settled more and more special cases of the final result. The construction of the linearly ordered compact space is extraordinarily complex, and to this date there is no simpler proof known.
![](https://celebratio.org/media/cunit/None_cunit_walter_memorial.jpg)
Mary Ellen was by consensus a dominant figure in general topology. Her results are difficult, deep, original, and important. The connections she found between topology and logic attracted many set-theorists and logicians to topology. The best general topologists and set-theorists in the world passed regularly through Madison to visit her and work with her and her students and colleagues.
She had eighteen PhD students, many of whom went on to have sterling careers of their own. To quote one of them, Michael Starbird, “From the perspective of a graduate student and collaborator, her most remarkable feature is the flood of ideas that is constantly bursting from her…. It is easy to use the Mary Ellen Rudin model to become a great advisor. The first step is to have an endless number of great ideas. Then merely give them totally generously to your students to develop and learn from. It is really quite simple. For Mary Ellen Rudin.”