An easy proof by contradiction concerning sets absorbing sequences; a proof that various statements about convergence of sequences in a non-empty set are equivalent to the set having exactly one point; various examples relating to (non) sequential compactness and divergence of subsequences.
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

An easy proof by contradiction concerning sets absorbing sequences; a proof that various statements about convergence of sequences in a non-empty set are equivalent to the set having exactly one point; various examples relating to (non) sequential compactness and divergence of subsequences. Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

Definitions, Proofs and Examples 5

These sessions are intended to reinforce material from lectures, while also providing more opportunities for students to hone their skills in a number of areas, including the following: working with formal definitions; making deductions from information given; writing relatively routine proofs; investigating the properties of examples; thinking up examples with specified combinations of properties.

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Education

These sessions are intended to reinforce material from lectures, while also providing more opportunities for students to hone their skills in a number of areas, including the following: working with formal definitions; making deductions from information given; writing relatively routine proofs; investigating the properties of examples; thinking up examples with specified combinations of properties. Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

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Definitions, Proofs and Examples 5

Definitions, Proofs and Examples 5