## Linear Operators, Part 1 |

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2 LEMMA. (a) In a topological group G, any algebraic combination of any number

of variables a 1, ..., a, is continuous as a map of GX. . . × G into G. (b) In a linear

2 LEMMA. (a) In a topological group G, any algebraic combination of any number

of variables a 1, ..., a, is continuous as a map of GX. . . × G into G. (b) In a linear

**topological space**3., all linear combinations of any number of scalars x1, ..., xm, ...Page 413

non-zero linear functional on the complex space 3., which separates the sets M

and N. Q.E.D. 2. Linear

1 are applied to linear

non-zero linear functional on the complex space 3., which separates the sets M

and N. Q.E.D. 2. Linear

**Topological Spaces**In this section, the results of Section1 are applied to linear

**topological spaces**. Statements 1–6 of this section are ...Page 419

Then the T topology of 3 is the topology obtained by taking as base all sets of the

form N(p; A, e) = {q|f(p)-f(q) < e, fe A), where ... If I' is a total linear space of linear

functionals on 3, 3 is a locally convex linear

Then the T topology of 3 is the topology obtained by taking as base all sets of the

form N(p; A, e) = {q|f(p)-f(q) < e, fe A), where ... If I' is a total linear space of linear

functionals on 3, 3 is a locally convex linear

**topological space**in its T topology.### What people are saying - Write a review

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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