Explore: Pontryagin Spaces

that Banach spaces and reflexive spaces, being considered as topological groups (with the additive group operation), satisfy Pontryagin duality. Later

Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin, first name sometimes anglicized as Leon) (3 September

In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential

\cdot \rangle } . Pontryagin spaces are named after Lev Semenovich Pontryagin. A symmetric operator A on an indefinite inner product space K with domain K

Nöbeling–Pontryagin theorem then states that such spaces with finite dimension are characterised up to homeomorphism as the subspaces of the Euclidean spaces,

the rational numbers. Metric spaces are also studied in their own right in metric geometry and analysis on metric spaces. Many of the basic notions of

Euclidean space implies T1 space". Mathematics Stack Exchange. Arkhangel'skii (1990). See example 21, section 2.6. A.V. Arkhangel'skii, L.S. Pontryagin (Eds

Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another

they call locally compact. Spaces satisfying condition (4) are exactly the locally compact regular spaces. Indeed, such a space is regular, as every point

Hausdorff spaces are also called T2 spaces. The name separated space is also used. A related, but weaker, notion is that of a preregular space. X {\displaystyle