The book, Inverse Limits: From Continua to Chaos,
co-authored with Bill Mahavier is now in print, published by Springer
as volume 25 in their Developments in Mathematics series. As part of
preparing that book, I compiled a
bibliography on inverse limits in pdf format. The list includes some
entries that are not inverse limit specific. I would appreciate being
notified of omissions (including preprints) in the list at my mst.edu
email address.
Another book, An Introduction to Inverse Limits with Set-valued
Functions, is now in print in the Springer Briefs series.
Each of these books contains an error that readers should be aware
of. An error in the Springer Brief has recently come to my attention. See
the corrigendum for information.
I have compiled a bibliography
on inverse limits with set-valued functions. I would appreciate having
any omissions brought to my attention also at my mst.edu email address. I
would also like to include any preprints on the subject in the bibliography
so let me know of any publications or preprints that have been omitted.
The Topology Seminar at the University of Houston ran from 1972 until 1989. Extensive notes were kept of the presentations in the seminar. The complete text of the two notebooks recording the proceedings of the seminar has been scanned and is available for download, see Book 1 and Book 2. These scans are also available available courtesy of the Department of Mathematics and Statistics at Missouri University of Science and Technology (formerly, the University of Missouri--Rolla) and the libraries at Missouri S&T and UM--Columbia at https://mospace.umsystem.edu/xmlui/handle/10355/70301. The books are permanently housed in the Archives of American Mathematics at the University of Texas in Austin and also permanently available at https://hdl.handle.net/10355/70301. The problems raised in the seminar formed the basis of the Houston Problem Book [see Continua with the Houston Problem Book, Lecture Notes in Pure and Applied Mathematics, volume 170, Marcel-Dekker, 1995].
A picture representing the third
composite of a mapping of a
simple triod onto itself which I constructed in order to obtain an
atriodic tree-like continuum with positive span may be viewed by
clicking on the word "mapping". An explanation of the schematic representation of
the map may be seen by clicking on the word "explanation".
On a trip to Oaxaca, Mexico, in December, 1997, I took a picture of an interesting street sign showing an "application" of continua in Mexico. ;-)
The background on this page is an electronically embossed view of the Rolla Building. The Rolla Building is the oldest building on the campus but it has recently been renovated and is now the home of the Department of Mathematics and Statistics. Here are some pictures of the Rolla Building. Some of the pictures were made before the turn of the century while some were made as recently as October, 1997. A brief history of the building is available as well.
Papers involving inverse limits with set-valued bonding functions include one with Mahavier on set-valued inverse limits, one on unions of mappings, one on problems and partial solutions, one on nonconnected inverse limits with a single function, one on nonconnectedness with sequences of functions (with M. Marsh), one on chainability of inverse limits with set-valued functions, one on treelikeness, one on dimension and treelikeness (Houston J. 2014), and one on inverse limits with families of upper semi-continuous functions (Boletin SMM, Mexico 2014). Here is a copy of a paper from Topology Proceedings on the effect of dimension one on set-valued inverse limits.
I recently gave two lectures at Missouri S&T. One of them was intended for a general audience and is reproduced here.
The text of a paper on the history of continuum theory based on a talk in Birmingham, AL, several years ago is posted here. Other papers include a paper on non-planar tree-like continua and a paper on open problems in topology.
Recent preprints involving set-valued inverse limits include papers on graphs that are arcs, graphs that are sinusoids, and a survey on some traditional topics in continuum theory arising in such inverse limits.
Copies of three of my papers that are not very accessible may be downloaded here. One is on a characterization of indecomposability (with H. Cook) from the book, Topology Conference, Arizona State University (the first Spring Topology Conference). Two others are from Topology Conferences at the University of Louisiana at Lafayette, one on span of tree-like continua and the other on atriodic tree-like continua. These last two papers were published in their conference proceedings.
Here are some pictures from the Spring Topology and Dynamics conference held in Milwaukee, March 2008. I took some B&W pictures at the Spring Topology Conference in Houston in 1971.
Here is a link to some of my photographs.
www.flickr.com
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