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Unformatted text preview: • The characterization of compact in terms of open covers (Theorem 3.3.8) • The Sequential Criterion for Functional Limits • Algebraic Limit Theorem for Functional Limits • The Divergence Criterion for Functional Limits • Characterizations of Continuity (Theorem 4.3.2) • The Discontinuity Criterion • Algebraic Continuity Theorem • Composition of Continuous Functions • Preservation of Compact Sets • Extreme Value Theorem The exam may have: • One question that asks you for deﬁnitions or statements of theorems. • One question that is very similar to homework problems • One question that asks you for examples • One question that asks you to prove something about functional limits • Other questions...
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- Winter '08
- Topology, Metric space, Compact space, General topology, Algebraic Limit Theorem, functional limits