Ernest Michael
Encyclopedia
Ernest A. Michael is an American mathematician who is best known for the Michael selection theorem, which he proved in . He received his Ph.D. from the University of Chicago
in 1951. He wrote his dissertation on "Locally m-convex algebras" under the supervision of Irving Segal
. He had 5 doctoral students and 16 doctoral descendants. He wrote over 100 papers, mostly in the area of functional analysis
.
Michael is also known in topology
for the Michael line, a paracompact space
whose product
with the topological space
of the irrational numbers is not normal
.
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in 1951. He wrote his dissertation on "Locally m-convex algebras" under the supervision of Irving Segal
Irving Segal
Irving Ezra Segal was a mathematician known for work on theoretical quantum mechanics.He was at the Massachusetts Institute of Technology...
. He had 5 doctoral students and 16 doctoral descendants. He wrote over 100 papers, mostly in the area of functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
.
Michael is also known in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
for the Michael line, a paracompact space
Paracompact space
In mathematics, a paracompact space is a topological space in which every open cover admits a locally finite open refinement. Paracompact spaces are sometimes also required to be Hausdorff. Paracompact spaces were introduced by ....
whose product
Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology...
with the topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
of the irrational numbers is not normal
Normal space
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space...
.