Topics in Functional Analysis

Course Description

A generalization of the main notions and concepts of analysis, geometry and algebra. Topics include operators (functions), metric and topological spaces, complete spaces, completion of metric spaces, contraction mapping principle, separable spaces, compactness of sets and criteria of compactness in a metric spaces, linear spaces and linear operators, linear normed spaces, finite spaces and subspaces, abstract Hilbert spaces, linear operators in linear normed spaces, space of linear operators.

Learning Outcomes

  • Evaluate operators, metric spaces.
  • Prove the Contraction Mapping Theorem.
  • Elaborate the main concepts of the compactness.
  • Explore the properties of linear spaces and linear operators.
  • Explore the Banach spaces.
  • Investigate Hilbert spaces.
  • Elaborate the theorem on inverse operators and its applications.


Why Choose National University?

We’re proud to be a veteran-founded, San Diego-based nonprofit. Since 1971, our mission has been to provide accessible, achievable higher education to adult learners. Today, we educate students from across the U.S. and around the globe, with over 185,000 alumni worldwide.

Four-Week Courses

Focus on one subject at a time — one month at a time — and finish your degree faster.

75+ Degree Programs

Choose from associate, bachelor’s, and master’s degrees, plus credentials and certificates.

On Campus or Online

Study when and where it’s convenient for you with evening, weekend, and 100% online classes.

Year-Round Enrollment

Apply or transfer any time. Classes start monthly, and applications are accepted year round.

20+ Locations

Attend class and learn onsite at one of over 20 locations in California.

Military Friendly

As a Yellow Ribbon school, we offer tuition discounts to servicemembers and dependents.

School of Arts, Letters, and Sciences

“Our faculty are established scholars and creators in their own fields. They are dedicated to making your entry into their disciplines a successful one, preparing you for your career as well as graduate study.”
School of Arts, Letters, and Sciences
Jackson M., Class of 2021, Military Veteran
Chat with an Advisor
National University
Chat Options