In this program
- Normed spaces and completeness
- Banach spaces
- Linear operators
- Operator norm
- Hilbert spaces and orthogonality
- Riesz representation
- Hahn–Banach
- Open mapping theorems (introduction)
Banach and Hilbert spaces
Open mapping theorems (introduction)
Graduate analysis · Theoretical / proof-based
Topic
Open mapping theorems (introduction)
Graduate Analysis — scope drawn from Axler Measure, Integration & Real Analysis (open access), Bass Real Analysis for Graduate Students (free PDF), and typical first-year graduate analysis syllabi.