筑波大学トポロジーセミナー
世話人：川村一宏，平山至大，石井敦，丹下基生，蓮井翔
| 日時 | ２０１５年８月２７日（木）１６：３０～１７：３０ |
|---|---|
| 場所 | 筑波大学 自然系学系D棟 D814 |
| 講演者 | Arkady Leiderman (Ben-Gurion University of the Negev, Israel) |
| 講演題目 | Basic families of functions and embeddings of free locally convex spaces |
| アブストラクト | Let X be a completely regular topological space. The free locally convex space on X is a locally convex space L(X) for which X forms a Hamel basis and such that every continuous mapping from X to a locally convex space E extends uniquely to a continuous linear operator from L(X) to E. In our talk we survey the results which are related to the following problem: characterize all topological spaces X such that L(X) can be embedded into L[0,1] as a linear subspace / a linear closed subspace, where [0,1] is a usual unit segment. The proofs are based on the Ostrand's theorem which generalizes the dimensional aspect of the Kolmogorov's Superposition Theorem: every n-dimensional metrizable compact can be basically embedded into the cube [0,1]^{2n+1}. |
| その他 |
