Course title  Topology 1 

Course code  KAG/T1 
Organizational form of instruction  Lecture + Exercise 
Level of course  Bachelor 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  3 
Language of instruction  Czech 
Status of course  Compulsoryoptional, Optional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
1. Structures on sets. 2. Topological structures, open sets, interior, exterior, boundary points, bounded sets, base, subbase, Hausdorff space, first and second countability, continuous mappings, examples of topological structures, subspaces. 3. Structures on Euclidean spaces, topology of Euclidean spaces, examples of open sets, epsilondelta definition of a continuous function, examples of continuous and noncontinuous mappings. 4. Comparison of topologies, final and initial topologies, product topology, quotient topology, examples: factorization of the squere. 5. Metric topology, open ball, properties of the metric topology, bopunded sets. 6. Compact topological spaces, continuous mappings of compact spaces, extrema of continuous functions, examples: criterion of compactness in Euclidean spaces, spheres. 7. Connected spaces, examples of connected and nonconnected spaces. 8. Applications: Topological groups, topological vector spaces, manifolds.

Learning activities and teaching methods 
Lecture, Work with Text (with Book, Textbook) 
Learning outcomes 
Generalization of properties of metric spaces to topological spaces, metrizability, continuous mappings.
1. Knowledge Define basic topological concepts 
Prerequisites 
Principles of the set theory and metric spaces.

Assessment methods and criteria 
Mark, Oral exam

Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Faculty of Science  Teaching Training in Descriptive Geometry for Secondary Schools (2015)  Pedagogy, teacher training and social care  1  Winter 
Faculty of Science  Mathematics (1)  Mathematics courses  3  Winter 
Faculty of Science  Mathematics and Applications (1)  Mathematics courses  3  Winter 
Faculty of Science  Discrete Mathematics (2015)  Mathematics courses  2  Winter 
Faculty of Science  Applied Mathematics (2014)  Mathematics courses  1  Winter 