Ernest A. Michael (August 26, 1925 – April 29, 2013) was a prominent American mathematician known for his work in the field of

general topology In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geomet ...

, most notably for his pioneering research on set-valued mappings. He is credited with developing the theory of continuous selections. The

Michael selection theorem In functional analysis, a branch of mathematics, Michael selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: : Let ''X'' be a paracompact space and ''Y'' a Banach space. :Let F ...

is named for him, which he proved in . Michael is also known in

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

for the Michael line, a

paracompact space In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, ...

whose

product Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Produ ...

with the

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...

of the

irrational numbers In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integ ...

is not

normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...

. He wrote over 100 papers, mostly in the area of

. Michael was born in Zürich, Switzerland, August 26, 1925, to

Ashkenazi Jewish Ashkenazi Jews ( ; he, יְהוּדֵי אַשְׁכְּנַז, translit=Yehudei Ashkenaz, ; yi, אַשכּנזישע ייִדן, Ashkenazishe Yidn), also known as Ashkenazic Jews or ''Ashkenazim'',, Ashkenazi Hebrew pronunciation: , singu ...

parents, Jacob and Erna Michael. He lived in

Berlin, Germany Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent ...

, until 1932. Anticipating the burgeoning threat of Nazism, his family moved to

The Hague, Netherlands The Hague ( ; nl, Den Haag or ) is a city and municipality of the Netherlands, situated on the west coast facing the North Sea. The Hague is the country's administrative centre and its seat of government, and while the official capital of ...

, and then to New York in 1939. Michael attended Horace Mann High School, graduating at age 15. His undergraduate career at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

was interrupted when he enlisted in the

United States Navy The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage ...

(1944–46), where he served aboard the USS ''Kwajalein''. He returned to Cornell, where he received his B.A. in 1947. He earned his M.A. from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

in 1948, and Ph.D. from The

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

in 1951, writing his dissertation titled ''Locally Multiplicatively-Convex Topological Algebras'' under the supervision of

Irving Segal Irving Ezra Segal (1918–1998) was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for h ...

. Michael was a member of the Department of Mathematics at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...

(assistant professor 1952–56, associate professor 1956–60, professor 1960) for over 40 years, from 1952 until his retirement in 1993. He was also a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

(1951–52, 1956–57, 1960–61, 1968–69),

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

(1973–74) and

University of Stuttgart The University of Stuttgart (german: Universität Stuttgart) is a leading research university located in Stuttgart, Germany. It was founded in 1829 and is organized into 10 faculties. It is one of the oldest technical universities in Germany wit ...

(1978–79). In 2012 he became an inaugural fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-02-04. Michael died in 2013 at the age of 87.

Selected works

References

{{DEFAULTSORT:Michael, Ernest 20th-century American mathematicians 21st-century American mathematicians American people of German-Jewish descent Institute for Advanced Study visiting scholars Mathematical analysts Topologists University of Chicago alumni Fellows of the American Mathematical Society 1925 births 2013 deaths Harvard University alumni Cornell University alumni Horace Mann School alumni Mathematicians from New York (state)