Course title  Chapters in Topology II 

Course code  MU/03264 
Organizational form of instruction  Lecture + Lesson 
Level of course  Master 
Year of study  not specified 
Semester  Summer 
Number of ECTS credits  6 
Language of instruction  Czech, English 
Status of course  Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


Course content 
1. Uniform spaces (multivalued functions, entourages, induced topology, uniform continuity). 2. Complete spaces and completion (Cauchy filters, minimal Cauchy filters, completeness, theorem on completion, completeness and completion of subspaces and products). 3. Compactness and uniform structure (uniformity of compact spaces, precompactness, compactness of uniform spaces, compact sets in uniform spades). 4. StoneČech theorem (evaluation mapping, compactification, StoneČech theorem). 5. Ascoli theorem (uniform convergence, equicontinuity, Ascoli theorem).

Learning activities and teaching methods 
unspecified 
Recommended literature 

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

Mathematical Institute in Opava  Geometry and Global Analysis (1)  Mathematics courses  1  Summer 
Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  4  Summer 
Mathematical Institute in Opava  Mathematical Analysis (1)  Mathematics courses  1  Summer 