General and Differential Topology in Graduate School level

This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Content: Topological and metric spaces, continuity, subspaces, products and quotient topology, compactness and connectedness, extension theorems, topological groups, topological and differentiable manifolds, tangent spaces, vector fields, submanifolds, inverse function theorem, immersions, submersions, partitions of unity, Sard's theorem, embedding theorems, transversality, classification of surfaces. --- (See attached file for full problem description)

General and Differential Topology in Graduate School level

This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Content: Topological and metric spaces, continuity, subspaces, products and quotient topology, compactness and connectedness, extension theorems, topological groups, topological and differentiable manifolds, tangent spaces, vector fields, submanifolds, inverse function theorem, immersions, submersions, partitions of unity, Sard's theorem, embedding theorems, transversality, classification of surfaces. --- (See attached file for full problem description)

General and Differential Topology in Graduate School level

This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Content: Topological and metric spaces, continuity, subspaces, products and quotient topology, compactness and connectedness, extension theorems, topological groups, topological and differentiable manifolds, tangent spaces, vector fields, submanifolds, inverse function theorem, immersions, submersions, partitions of unity, Sard's theorem, embedding theorems, transversality, classification of surfaces. --- (See attached file for full problem description)

General and Differential Topology

Find conditions under which the box topology is strictly finer than the product topology. See attached file for full problem description.

General and Differential Topology in Graduate School level

This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Content: Topological and metric spaces, continuity, subspaces, products and quotient topology, compactness and connectedness, extension theorems, topological groups, topological and differentiable manifolds, tangent spaces, vector fields, submanifolds, inverse function theorem, immersions, submersions, partitions of unity, Sard's theorem, embedding theorems, transversality, classification of surfaces. --- (See attached file for full problem description)