## Lectures on Locally Convex Vector Spaces |

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### Contents

B Topological Spaces S? | 7 |

Linear Spaces 111 | 18 |

Linear Topological Spaces | 24 |

2 other sections not shown

### Common terms and phrases

algebraic automorphism Banach bornological bounded set bounded subset Cauchy sequence closed convex closure compact subset complete completeo containing continuous linear form continuouso convex direct sum convex hull convex set Corollary Corollaryo countable cr[u defined definition denote dense direct sum topology disk space dual system elements equicontinuous finer form f function fundamental system hence homomorphism hyperplane hyperplane H implies intersection isomorphic lattice Let H linear space linear subspace linear topological space locally convex direct locally convex space locally convex topology metrizable neighborhood basis neighborhood of 9 non-empty norm numbers open set partially ordered partially ordered linear positive linear form precompact product topology Proof quotient space quotient topology radial real hyperplane relatively compact Remark resp respect respo restriction satisfies scalar semi-norms simple convergence subset of F Theorem topology induced topology of simple topology of uniform uniform convergence weakly