Course title  Functional Analysis I 

Course code  MU/02025 
Organizational form of instruction  Not filled in + Not filled in 
Level of course  Bachelor 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  6 
Language of instruction  Czech 
Status of course  Compulsory 
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. Topological vector spaces (conservation of algebraical properties by topological operations, properties of neighbourhoods of zero in a topological vector space, continuous linear mappings of topological vector spaces). 2. HahnBanach theorem (convex sets, convex functions, Jensen inequality, sublinear functions, Minkowski function, HahnBanach theorem, locally convex spaces, seminorms, locally convex topology generated by seminorms, strict separation theorem). 3. Openness principle (Fréchet spaces, Banach theorem on open mapping, Banach theorem on inverse mapping, theorem on closed graph). 4. Boundedness principle (bounded sets, bounded operators, equicontinuity, equiboudedness and pointwise boundedness, BanachSteinhaus 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  Mathematical Analysis (1IVT)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Mathematics (2F)  Mathematics courses  3  Winter 