- M55: Exercise sheet 7 More on components
- M55: Exercise sheet 2 1. Let X be the Sierpinski 2-point space and f : X ! R a continuous map. Show that
- M55: Exercise sheet 8 1. Make suitable simpli cations to identify the following surfaces
- M55: Exercise sheet 0 (revision of set theory) Let X;Y be sets. I hope the following concepts and notations are familiar
- M55: Exercise sheet 6 Alexandro one-point compacti cation
- M55: Exercise sheet 3 1. Let A be a closed subset of a topological space X and F A. Show that F is*
- M55: Exercise sheet 0 (revision of set theory) Let X, Y be sets. I hope the following concepts and notations are familiar
- M55: Exercise sheet 6 Alexandroff one-point compactification
- M55: Exercise sheet 4 1. Let A X and B Y be closed subsets of topological spaces X and Y .
- Harmonic tori in spheres and complex projective spaces F. E. Burstall
- M55: Exercise sheet 5 1. Let X be a set. What is the coarsest topology on X for which all singleton sets are
- M55: Exercise sheet 3 1. Let A be a closed subset of a topological space X and F A. Show that F is closed
- M55: Exercise sheet 1 1. (a) Let (X; d) be a metric space. Show that if x 6= y 2 X then there are metric open
- Riemannian Twistor Spaces and Holonomy Groups Francis Burstall
- From: "Geometry of low-dimensional manifolds: 1", C.U.P. (1990), pp. 231--235 Minimal surfaces in quaternionic symmetric spaces
- TWISTOR SPACES FOR RIEMANNIAN SYMMETRIC SPACES Francis Burstall, Simone Gutt and John Rawnsley
- Basic Riemannian Geometry F.E. Burstall
- SUBMANIFOLD GEOMETRY IN GENERALIZED FLAG MANIFOLDS FRANCIS E. BURSTALL AND DAVID M. J. CALDERBANK
- From: "Geometry of low-dimensional manifolds: 1", C.U.P. (1990), pp. 231--235 Minimal surfaces in quaternionic symmetric spaces
- HERMITIAN STRUCTURES ON HERMITIAN SYMMETRIC SPACES F. Burstall , O. Mu skarov , G. Grantcharov and J. Rawnsley
- Harmonic tori in Lie groups Francis E. Burstall
- ISOTHERMIC SURFACES IN ARBITRARY CO-DIMENSION F. E. Burstall
- M7: Exercise sheet 1 1. Prove directly from axioms (A1)(A9) that, for all a, b, c R,
- M7: Exercise sheet 3 On denseness
- M7: Exercise sheet 5 On Cauchy sequences
- M7: Exercise sheet 9 1. For each of the power series1 below, find the radius of convergence
- M40: Exercise sheet 2 (mostly about topological groups) 1. Let X, Y be topological spaces and let A X, B Y have the induced topology.
- M40: Christmas exercise sheet Some revision questions
- M55: Exercise sheet 0 (revision of set theory) Let X, Y be sets. I hope the following concepts and notations are familiar
- M55: Exercise sheet 2 1. Let X be the Sierpinski 2-point space and f : X R a continuous map. Show that
- M55: Exercise sheet 3 1. Let A be a closed subset of a topological space X and F A. Show that F is closed
- M55: Exercise sheet 7 More on components
- M11: Exercise sheet 10 1. Suppose that f : [a, b] R is a bounded function which is continuous on (a, b). Show
- Basic Riemannian Geometry F.E. Burstall
- TWISTOR SPACES FOR RIEMANNIAN SYMMETRIC SPACES Francis Burstall, Simone Gutt and John Rawnsley
- HERMITIAN STRUCTURES ON HERMITIAN SYMMETRIC SPACES F. Burstall
- Harmonic tori in Lie groups Francis E. Burstall
- Harmonic maps and soliton theory Francis E. Burstall
- Riemannian Twistor Spaces and Holonomy Groups Francis Burstall
- ISOTHERMIC SURFACES IN ARBITRARY CO-DIMENSION F. E. Burstall
- Harmonic maps and soliton theory Francis E. Burstall
- M55: Exercise sheet 8 1. Make suitable simplifications to identify the following surfaces
- M55: Exercise sheet 5 1. Let X be a set. What is the coarsest topology on X for which all singleton sets are
- M40: Exercise sheet 1 (mostly revision) 1. Let X be a topological space and A, B be closed subsets of X such that A B = X.
- M11: Exercise sheet 8 More on series of functions
- M40: Exercise sheet 4 1. (a) Show that homotopy is an equivalence relation on continuous maps from X to Y .
- M7: Exercise sheet 8 1. Let p > 0 and x R. By applying the vanishing test to a certain convergent series,
- M40: Exercise sheet 6 1. Show that the retraction defined in the Brouwer Fixed Point Theorem is indeed con-
- M11: Exercise sheet 11 1. Prove that, for a, b > 1,
- M55: Exercise sheet 6 Alexandroff one-point compactification
- Harmonic tori in Lie groups Francis E. Burstall
- ISOTHERMIC SURFACES IN ARBITRARY CO-DIMENSION F. E. Burstall
- Basic Riemannian Geometry F.E. Burstall
- M55: Exercise sheet 1 1. (a) Let (X, d) be a metric space. Show that if x = y X then there are metric open
- M40: Exercise sheet 7 1. Let p : E X be a covering space and consider the action of 1(X, x0) on p-1({x0}).
- M40: Exercise sheet 5 1. (a) Let A X be a deformation retract of X. Show that the inclusion i : A X is
- M40: Exercise sheet 3 1. Show that a path-connected space is connected.
- M11: Exercise sheet 6 1. Let f : I R be twice differentiable on an open interval I.
- M11: Exercise sheet 1 M7 style things
- TWISTOR SPACES FOR RIEMANNIAN SYMMETRIC SPACES Francis Burstall, Simone Gutt and John Rawnsley
- Harmonic tori in spheres and complex projective spaces F. E. Burstall
- Riemannian Twistor Spaces and Holonomy Groups Francis Burstall
- Harmonic maps and soliton theory Francis E. Burstall
- From: "Geometry of low-dimensional manifolds: 1", C.U.P. (1990), pp. 231--235 Minimal surfaces in quaternionic symmetric spaces
- HERMITIAN STRUCTURES ON HERMITIAN SYMMETRIC SPACES F. Burstall*, O. Mu~skarov**, G. Grantcharov** and J. Rawnsley*