Topology

Cod: 21117

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

We extend the usual notions of distance, limit and continuity, first to metric spaces and then to topological spaces.

Metric Spaces

Topological spaces

Topological spaces

Upon concluding this Curricular Unit the student should be able to:

Identify and be able to properly use the main topological concepts in metric and topological spaces.

Identify and be able to properly use the main topological concepts in metric and topological spaces.

1. Review of topological concepts in R.

2. Metric spaces. Definition and examples.

3. Topological concepts in metric spaces.

4. Topological spaces. Definition and examples.

5. Topological concepts in topological spaces.

2. Metric spaces. Definition and examples.

3. Topological concepts in metric spaces.

4. Topological spaces. Definition and examples.

5. Topological concepts in topological spaces.

Folhas de apoio disponibilizadas online.

1.Wilson A. Sutherland, Introduction to Metric and Topological Spaces, Oxford University Press, 2nd Edition, 2009.

2. G. F. Simmons, Introduction to Topology and Modern Analysis, International Student Edition, McGraw-Hill, 1963.

3. A.N. Kolmogorov & S.V. Fomin, Elementos da Teoria das Funções e de Análise Funcional, Editora MIR, 1982.

E-learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).

Students are assumed to be conversant with the subject matter studied in Elements of Infinitesimal Analysis I and II.