Code: | M3008 | Acronym: | M3008 | Level: | 300 |
Keywords | |
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Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Mathematics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:B | 0 | Official Study Plan | 3 | - | 6 | 56 | 162 |
L:M | 10 | Official Study Plan | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:Q | 0 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |
Topological spaces: the topology on a space. Examples of topological spaces. The metric spaces. Comparison of topologies. Comparison of metrics. Equivalent metrics. Continuous functions. Continuity and convergence in metric spaces. Homeomorfismos. Supremum of a family of topologies. The topology generated by a collection of parts of a set X. Numerabilidade axioms.
Construction of topological spaces: Initial Topology. Subspaces.Embeddings. Initial topology for a family of maps. Product topology (Tychonoff) and the box topology. Characterization of the product topology. Final topology. Quotient spaces/identification Topology. Examples of quotient spaces. Final topology for a set of maps. Sum topology. Unions of locally finite families of closed sets.
Topological Properties, Invariants: Connected spaces. Path connecteness. Locally connected spaces and locally path connected spaces. Separation axioms. Spaces T0, T1, T2, regular, completely regular and normal. Compact spaces. Compacts in Euclidean Spaces. Sequentially compact spaces. Uniform continuity. Compact and normality. Tychonoff's theorem (demonstration in the finite case). Lebesgue number . Lebesgue's lemma. Locally compact spaces and regularity. Product of metric spaces. Compactifications. Complete metric spaces. Product of complete spaces; complete spaces and compactness; Banach's fixed point theorem. Contraction mappings. Baire’s theorem.Applications of Banach's fixed point theorem.
designation | Weight (%) |
---|---|
Exame | 100,00 |
Total: | 100,00 |
Terms of frequency: If the limit of absences is exceeded the student will not be admited access to examination, either in time or normal use (except for students exempted from frequency)
Formula Evaluation: There wil be two components of assessment:
• Continuous Evaluation (optional): based on test results and itcan be corrected by the assessment practices in the classroom (including level of participation and performance in class) *.
• Final written exam
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The evaluation will be done through two tests required and the final exam. Admission to the second test will be conditional upon a minimum grade of 8.0 values.
Minimum grade of second test 6 values
The tests may replace the exam.
The notice of exemption will not necessarily be the arithmetic mean of test scores *
The student with a grade exceeding eighteen values in tests or final examination may eventually be subjected to an extra proof.
For students under normal conditions with access to examination and which have succeeded the distributed evaluation( score above or equal to 10/20), the final classification is obtained by the highest ranking achieved in the distributed evaluation and / or examination
According to the General Evaluation Rules.
According to the General Evaluation Rules.