## 27008 - General Topology

### Syllabus Information

2017/18
Subject:
27008 - General Topology
Faculty / School:
Degree:
453 - Degree in Mathematics
ECTS:
9.0
Year:
2
Semester:
Annual
Subject Type:
Compulsory
Module:
---

### 5.1. Methodological overview

The learning process is based in the following items:

- Theoretical Lectures,
- Problem sessions.

Theoretical Lectures.
Participative problem sessions.

Semipresential learning through the Moodle page of the subject; moodle.unizar.es  (acces restricted to students enrolled in the subject).

### 5.3. Syllabus

GENERAL TOPOLOGY

1.- METRIC SPACES (I): Normed linear spaces. Metric spaces. Limit point, Derived and Closure set. Open sets.

2.- TOPOLOGICAL SPACES: Topological spaces. Bases and subbases. Interior, derived set, clousure and frontier.

3.- CONTINUOUS FUNCTIONS: Relative topology and subspaces. Open and closed maps, homeomorphisms. Product spaces. Quotient spaces.

4.- SEPARATION AND COUNTABILITY: Hausdorff spaces. Regular spaces. Normal spaces. Countability properties and related concepts.

5.- COMPACTNESS: Compact spaces. Locally compact spaces. Alexandroff compactification. Countably and sequentally compact spaces.

6.- METRIC SPACES (II): Compactness in metric spaces. Complete metric spaces. Completion of a matric space.

7.- CONNECTEDNESS: Connected spaces. Locally connectes spaces. Pathwise connected spaces. The homotopy relation.

8.- HOMOGENEOUS SPACES: Topological groups. Topological transformations groups. Topology of linear groups.

### 5.4. Course planning and calendar

Schedules of lectures and problems will coincide with the officially established and will be available at: https://ciencias.unizar.es

### 5.5. Bibliography and recommended resources

• Dugundji, James. Topology / James Dugundji Boston : Allyn and Bacon, 1966
• Higgins, P. J.. Introduction to topological groups / P. J. Higgins Cambridge : University Press, 1974
• Munkres, James R. Topología / James R. Munkres; traducción, Ángel Ferrández Izquierdo ... [et al.] . - 2ª ed. Madrid : Prentice Hall, D.L. 2001
• Willard, Stephen. General topology / Stephen Willard . - [1st. ed.] Reading, Massachusetts [etc.] : Addison-Wesley, cop. 1970