Colloquium Announcement
Department of Mathematics
West Virginia University
for
Thursday, September 24,1998, at 3:45pm
in 315 Armstrong Hall
(Tea and cookies begin at 3:00 in coffee room.)
Professor Jerzy Wojciechowski
WVU
Darboux-like Functions
The talk will be suitable for a general audience.
Students are strongly encouraged to participate.
Abstract
As we teach in Calculus, continuous functions from R to R have
the Intermediate Value Property. The functions with Intermediate Value
Property are called Darboux functions. It is easy to see that there are
Darboux functions that are not continuous. For example any derivative is a
Darboux function. During the talk we are going to define other classes of
functions that fall between the class of continuous functions and the class
of Darboux functions. We are going to consider generalizations of these
concepts to functions from Rn to R. Such classes have
unexpectedly nice properties with respect to algebraical addition. A recent
result of Chris Ciesielski and myself, augmented by a result of Francis Jordan,
shows that any set theoretic function from Rn to R can
be written as the algebraic sum of n+1 such Darboux-like functions but in
general n functions is not enough.
The information on the future (and past) Colloquia can be also found on web at the
address:
http://www.math.wvu.edu/homepages/kcies/colloquium.html