Mathematical Treasure: Mary Ellen Rudin’s Lectures on Set Theoretic Topology

Mary Ellen (Estill) Rudin (7 December 1924–18 March 2013), esteemed professor at the University of Wisconsin–Madison and prominent set-theoretic topologist, was the author of Lectures on Set Theoretic Topology [Rudin 1975], an important work in the late 20th-century development of topology using techniques from set theory and logic. She has been regarded “by consensus a dominant figure in general topology. Her results are difficult, deep, original and important” [Benkart et al. 2015, p. 629].

Figure 1. Mary Ellen Rudin at the International Congress of Mathematicians, Kyoto, Japan, 1990.
Photo courtesy of Ali Eminov, used with permission.

An undergraduate student of the famed mathematics educator R. L. Moore at the University of Texas, where she also received her PhD in 1949, she taught for a time at Duke University’s women’s college. There she met the Austrian-born Walter Rudin. The two married in 1953, and then moved to Madison in 1959, where Walter secured a position as a young professor of mathematics at the University of Wisconsin. Mary Ellen was hired as a part-time lecturer at first in the same department, while she raised the Rudins’ four children—and simultaneously supervised graduate students! In 1971 she was made a full professor at Wisconsin, where she went on to guide at least 18 doctoral students [Mathematics Genealogy Project n.d.].

Figure 2. Mary Ellen Rudin lecturing in China, 1981. Photo courtesy of Ali Eminov, used with permission.

As her friend and colleague Judith Roitman told it, Mary Ellen Rudin was

a woman mathematician at a time when there were few women mathematicians. She belonged . . . to what she called the housewives’ generation: women who did substantial mathematics outside the academy, with only occasional ad hoc positions [and] exhibiting enormous strength of character. . . . They thought of themselves as simply doing mathematics. [Benkart et al. 2015, p. 622]

Rudin was celebrated for her construction in 1955 of an example of a Dowker space (a normal space whose product with the unit interval is not normal), for her use of the box product as a way to construct spaces with interesting properties, and for her work with ultrafilters. Late in her career, nearly a decade after her retirement from Wisconsin, she resolved Nikiel’s conjecture, “characterizing the continuous images of compact ordered spaces as compact monotonically normal spaces” [Benkart et al. 2015, p. 626].

Her lectures on set-theoretic topology at the 1974 Conference Board of the Mathematical Sciences (CBMS) Regional Conference in Laramie, Wyoming, were published soon afterwards in monograph form [Rudin1975]. Franklin Tall reported that this work “established a framework” for further development in set-theoretic topology [Benkart et al. 2015, p. 625].

Figure 3. Title page from Lectures on Set Theoretic Topology [Rudin 1975].

On the opening page of the monograph, Rudin stated that “the set theoretic influence on general topology is an exciting, effective change,” and that “a real revolution has been going on . . . because of renewed interaction with set-theory” in topology.

Figure 4. Page 1 of Lectures on Set Theoretic Topology [Rudin 1975].

Figure 5. On page 49, Rudin considered the existence of a Dowker space [Rudin 1975].

Figure 6. Rudin identified properties of box product spaces on page 55 and following [Rudin 1975].

Readers interested in more information about Rudin’s life and career should consult [Benkart et al. 2015] and [Gruenhage and Nyikos 2015].

Images of the pages from Lectures on Set Theoretic Topology used in this article are courtesy of the Xavier University Library and used with permission. Convergence is also grateful to Rudin’s daughter, Catherine Rudin, and son-in-law, Ali Eminov, for sharing family photos from Eminov’s Flickr site. The images on this page may be used in your classroom; please contact the owners for all other uses.

REFERENCES

Benkart, Georgia, Mirna Džamonja, and Judith Roitman. 2015, June/July. Memories of Mary Ellen Rudin. Notices of the American Mathematical Society 62(6): 617–629.

Gruenhage, Gary, and Peter Nyikos. 2015. Mary Ellen Rudin—Remembrances. Topology and its Applications 195: 3–14.

Mathematics Genealogy Project. n.d. Mary Ellen Estill Rudin.

Rudin, Mary Ellen. 1975. Lectures on Set Theoretic Topology. Expository lectures from the CBMS Regional Conference held at the University of Wyoming, Laramie, WY, August 12–16, 1974. Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 23 Providence, RI: American Mathematical Society.