Paolo d'Alessandro is a former professor at the Department of Mathematics of the Third University of Rome (Italy).His primary research interests lie in System Theory (including foundations, linear time-variant and bilinear systems), Control Theory, Optimization,  Linear Programming and foundations of Probability and Stochastic Systems . He has made significant contributions to LP, by introducing various range space and conic methods for linear programming, and has also applied these results to control problems for linear dynamic systems.His current research focuses on extending methods to infinite-dimensional Optimization and applying range space and conic techniques to norm-optimal control of partial differential equations (PDEs).

• .- Introduction..- Basic Facts of Set Theory..- Linear Spaces..- Rudiments of General Topology..- Filters: the Fifth Equivalence..- Hahn Banach andSeparation Theorems..- Locally Convex and Barrelled Spaces..- Metrics and pseudometrics, Norms and Pseudonorms..- Topological Form of Hahn Banach and Separation Theorems..- Extreme points, Faces, Support and the KreinMilman Theorem..- Function Spaces.

Paolo d'Alessandro is a former professor at the Department of Mathematics of the Third University of Rome (Italy).His primary research interests lie in System Theory (including foundations, linear time-variant and bilinear systems), Control Theory, Optimization,  Linear Programming and foundations of Probability and Stochastic Systems . He has made significant contributions to LP, by introducing various range space and conic methods for linear programming, and has also applied these results to control problems for linear dynamic systems.His current research focuses on extending methods to infinite-dimensional Optimization and applying range space and conic techniques to norm-optimal control of partial differential equations (PDEs).

• .- Introduction..- Basic Facts of Set Theory..- Linear Spaces..- Rudiments of General Topology..- Filters: the Fifth Equivalence..- Hahn Banach andSeparation Theorems..- Locally Convex and Barrelled Spaces..- Metrics and pseudometrics, Norms and Pseudonorms..- Topological Form of Hahn Banach and Separation Theorems..- Extreme points, Faces, Support and the KreinMilman Theorem..- Function Spaces.

Paolo d'Alessandro is a former professor at the Department of Mathematics of the Third University of Rome (Italy).His primary research interests lie in System Theory (including foundations, linear time-variant and bilinear systems), Control Theory, Optimization,  Linear Programming and foundations of Probability and Stochastic Systems . He has made significant contributions to LP, by introducing various range space and conic methods for linear programming, and has also applied these results to control problems for linear dynamic systems.His current research focuses on extending methods to infinite-dimensional Optimization and applying range space and conic techniques to norm-optimal control of partial differential equations (PDEs).

• .- Introduction..- Basic Facts of Set Theory..- Linear Spaces..- Rudiments of General Topology..- Filters: the Fifth Equivalence..- Hahn Banach andSeparation Theorems..- Locally Convex and Barrelled Spaces..- Metrics and pseudometrics, Norms and Pseudonorms..- Topological Form of Hahn Banach and Separation Theorems..- Extreme points, Faces, Support and the KreinMilman Theorem..- Function Spaces.