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Compactness
Compactness
Bridget Dunbar
https://en.wikipedia.org/wiki/Compact_space
I think this website will be a good resource because of the diagrams shown to help explain. The sections are laid out in a simple manner that give the reader a chance to understand the basic concepts first that will be used to define compactness and its properties.
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https://terrytao.wordpress.com/2009/02/09/245b-notes-10-compactness-in-topological-spaces/
This website has a good layout. It describes the topic gives definitions and important facts, then gives examples and other lemmas/ corollaries that are important
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I think this website will be helpful because its people asking questions on parts of the topic they are confused on and others answering those questions.
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I do not think I will be able to use this one ^^^^^^
Additional Sources I could possibly use if the above two are not enough
http://www.mathcs.org/analysis/reals/topo/compact.html
MathCS.org – Real Analysis: 5.2. Compact and Perfect Sets
Exercises :
Elementary Real Analysis, Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner.
Prentice Hall, 2001, xv 735 pp.
page 172 number 4.5.10, 4.5.14, 4.5.15
page 173 number 4.5.16, 4.5.17, 4.5.21
Bridget Dunbar
December 15, 2017
Objective 3X Part 1
Compactness Arguments
The idea of compactness looks at the set as a whole to relate the ideas of closed and open sets.
Local Boundedness looks at the “local” assumptions. Suppose a function, f , is locally bounded at each point in set E. Meaning, that every point x ∈E there exists an interval (x-δ, x δ) and f is bounded on the points in E that belong to (x-δ, x δ).
The idea of local boundedness is expanded to relate to the while function:
|f(t)| ≤ Mx, ∀ t ∈ E in the interval (x-