(See attached file for full problem description with proper symbols and equations) --- • Let be the subspace of of all positive real numbers. Show that the map defined by is an identification map. ---
Continuous and identification maps
(See attached file for full problem description with proper symbols and equation) --- Let be a surjective continuous map between topological spaces. Show that: a) If f is an identification mp, then for any pace Z and any map the composition is continuous if and only if g is continuous. b) If, for any space Z and any ...continues
(See attached file for full problem description with proper symbols) --- Let and a map, given by . Let ~ be the equivalence relation on Xx[0,1] defined by and all other points are equivalent only to themselves. Show that Xx[0,1]/~ is homeomorphic to the Moebius strip. ---
(See attached file for full problem description with proper symbols) --- Let X and Y be topological spaces and let be a subspace. Show that 'homotopic relative A' defines an equivalence relation on the set of continuous maps from X to Y which agree with some fixed map on A. ---
(See attached file for full problem description with all symbols) --- Let X be a contractible space: a) Show that X is path connected b) Show that any two continuous maps where Y is any topological space, are homotopic. c) Let and be the map defined by . Show that and are homotopic. ---
Trivial Topology, Continuity and Connectedness
Let X and Y be topological spaces, where the only open sets of Y are the empty set and Y itself, i.e., Y has the trivial topology. • Show that any map X --> Y is continuous • Show that Y is path connected and simply connected. ---
Sets and Functions : Sets and Set Inclusion
Let U be the single-element set { 1 }. There are two subsets, the empty set φ and { 1 } itself. If A and B are arbitrary subsets of U, there are four possible relations of the form "A is subset of B". Count the number of true relations among these.
Sets and Functions : Subset Relations
Let U be the set { 1, 2 }. There are four subsets . List them. If A and B are arbitrary subsets of U, there are 16 possible relations of the form "A is subset of B". Count the number of true ones.
A boat travels in a direction of N40(deg) E for 3 hours at 20 mph. How far North and how far East did the boat travel? keywords: bearings
A tree casts a shadow 86 ft long when the angle of elevation of the sun is 48.7 degrees. Find the height of the tree.
