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Full-Text Articles in Mathematics

Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel Jan 2006

Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel

Mathematics Faculty Research Publications

These notes developed from a one semester course at Wayne State University, taught several times in the last three decades of the 1900s. The subject matter is analysis on manifolds, consisting of the theory of smooth manifolds, differential forms, integration of forms, the generalized Stokes' Theorem, de Rham cohomology, and some related topics. The course is intended for first or second year graduate students in Mathematics with a background in Advanced Calculus, General Topology, linear algebra (including quotient spaces), and a little elementary group theory (including some familiarity with the symmetric groups). Given the above background, the notes are self-contained. …

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A Topological Approach To Nonlinear Analysis, Wendy Ann Peske Jan 2005

A Topological Approach To Nonlinear Analysis, Wendy Ann Peske

Theses Digitization Project

A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.

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The Use Of Filters In Topology, Abdellatif Dasser Jan 2004

The Use Of Filters In Topology, Abdellatif Dasser

Electronic Theses and Dissertations

Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).

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The Topology Of Hyperbolic Attractors On Compact Surfaces, Todd L. Fisher Jun 2003

The Topology Of Hyperbolic Attractors On Compact Surfaces, Todd L. Fisher

Faculty Publications

Suppose M is a compact surface and M is a nontrivial mixing hyperbolic attractor for some f 2 Diff(M). We show that if is a hyperbolic set for some g 2 Diff(M), then is a nontrivial mixing hyperbolic attractor or repeller for g.

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1p Spaces, Anh Tuyet Tran Jan 2002

1p Spaces, Anh Tuyet Tran

Theses Digitization Project

In this paper we will study the 1p spaces. We will begin with definitions and different examples of 1p spaces. In particular, we will prove Holder's and Minkowski's inequalities for 1p sequence.

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A Density Property Of The Tori And Duality, Peter Loth Jan 2002

A Density Property Of The Tori And Duality, Peter Loth

Mathematics Faculty Publications

In this note, a short proof of a recent theorem of D. Dikranjan and M. Tkachenko is given, and their result is extended.

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Paracompact Subspaces In The Box Product Topology, Peter Nyikos, Leszek Piatkiwicz Jan 1996

Paracompact Subspaces In The Box Product Topology, Peter Nyikos, Leszek Piatkiwicz

Faculty Publications

No abstract provided.

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Describing And Distinguishing Knots, Lisa A. Padgett Jan 1995

Describing And Distinguishing Knots, Lisa A. Padgett

Theses Digitization Project

No abstract provided.

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Topologies And Cotopologies Generated By Sets Of Functions, Alan Dow, Melvin Henriksen, Ralph Kopperman, R. G. Woods Jan 1993

Topologies And Cotopologies Generated By Sets Of Functions, Alan Dow, Melvin Henriksen, Ralph Kopperman, R. G. Woods

All HMC Faculty Publications and Research

Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of Lx form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings.

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Review: J.R. Porter And R.G. Woods, Extensions And Absolutes Of Hausdorff Spaces (New York, Berlin, Heidelberg, 1987), Melvin Henriksen Jul 1989

Review: J.R. Porter And R.G. Woods, Extensions And Absolutes Of Hausdorff Spaces (New York, Berlin, Heidelberg, 1987), Melvin Henriksen

All HMC Faculty Publications and Research

Reviewed work: Jack R. Porter and R. Grant Woods. Extensions and absolutes of Hausdorff spaces. Springer-Verlag, New York, Berlin, Heidelberg, 1987, xiii + 856 pp., $89.00. ISBN 0-387-96212-3.

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Dupin Submanifolds In Lie Sphere Geometry, Thomas E. Cecil, Shiing-Shen Chern Jan 1989

Dupin Submanifolds In Lie Sphere Geometry, Thomas E. Cecil, Shiing-Shen Chern

Mathematics and Computer Science Department Faculty Scholarship

No abstract provided.

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