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Richard E. Hodel

Associate Professor Emeritus of Mathematics
Mathematics
Box 90320, Durham, NC 27708-0320
019 Physics Bldg, Durham, NC 27708

Overview


Professor Hodel is currently working on a number of projects. LOGIC, TOPOLOGY, MATROID THEORY: WHAT DO THEY HAVE IN COMMON? A quick answer: fundamental concepts in each of these branches of mathematics can be described in terms of a closure operator that satisfies certain axioms. These ideas are due to Tarski, Kuratowski, and Whitney respectively. We take a somewhat different approach and use the closely related notion of a nearness relation. This gives a somewhat more geometric approach to the ideas under discussion; numerous applications of this approach are obtained. A THEORY OF CONVERGENCE BASED ON KAPPA-NETS. This theory is very similar to convergence based on nets, but the directed set in question is always the collection of all finite subsets of some infinite cardinal kappa. This restriction allows one to take advantage of the eligence of the filter approach while retaining the intuitive advantage of nets. An immdediate application: a simplified cryptomorphic description of a topology in terms of convergence. This theory also yields characterizations of various covering properties (for example, Lindelof spaces) in terms of "generalized" kappa nets that have cluster points. INTRODUCTION TO MATHEMATRICAL LOGIC I am currently working on a second edition of my logic book.

Current Appointments & Affiliations


Associate Professor Emeritus of Mathematics · 2008 - Present Mathematics, Trinity College of Arts & Sciences

Recent Publications


Reflection theorems for cardinal functions

Journal Article Topology and Its Applications · January 1, 2000 This paper is a systematic study of reflection theorems for cardinal functions. There are four sections: theory of reflection; reflection theorems for c, e, s, hd, hL, L, d, and nw; reflection theorems for χ, t, ψ, and psw (assuming compactness); reflectio ... Full text Cite
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Recent Grants


Duke University Noyce Scholarship - Phase II

Inst. Training Prgm or CMECo Investigator · Awarded by National Science Foundation · 2013 - 2020

The Robert Noyce Fellows at Duke University

Inst. Training Prgm or CMECo-Principal Investigator · Awarded by National Science Foundation · 2005 - 2009

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Education, Training & Certifications


Duke University · 1962 Ph.D.
Davidson College · 1959 B.S.