We have to solve for x.

Solve for x: 4*+6* = 9* P.S * equals the X.

Verifying an Inner Product for Continuous Functions

Please see the attached file for the fully formatted problems. Suppose f(x) and g(x) are continuous real-valued functions defined for [0,1]. Define vectors in n, F= ( f(x1), f(x2), …,f(xn)) and G= g(x1), g(x2), …,g(xn)), where xk = k/n. Why is n = 1/n  f(xk) g(xk) dx not an inner product for the space o ...continues

Topology : Open Unit Balls

Please see the attached file for the fully formatted problems. Let , and denote the three metrics defined on . What are the open unit balls , and with respect to these three metrics? Make a sketch and describe them algebraically.

Counter Images of a Function

Please see the attached file for the fully formatted problems.

Topologies : Open Sets

• Let X:={a,b,c} be a set of three elements. A certain topology of X contains (among others) the sets {a}, {b}, and {c}. List all open sets in the topology T. • Let X’:={a,b,c,d,e} be a set of five elements. A certain topology T’ on X’ contains (among others) the sets {a,b,c}, {c,d} and {e}. List any other open set in T’ which ...continues

Topological Spaces : Continuity of Map

Let X and Y be topological spaces. Show that, if Y has the indiscrete topology, then any map f: X--> Y is continuous.

Abstract Analysis : Continuity of a Map

Show that phi is (infinite d,d) continuous where d is the standard metric... (See attachment for full question)

Continuity and Limit Points

1. For i = 1,2 let fi: Xi --> Yi be maps between topological spaces. Show that the product f1Xf2: X1XX2 --> Y1XY2 defined by f1Xf2(x1x2):= (f1(x1), f2(x2)) is continuous if and only if f1 and f2 are continuous. *(Please see attachment for proper representation of formulas and problem #2)

Subspace Topology: Interior, Closure, Boundary and Limit Points

Consider the following subsets of (FUNCTION1) and (FUNCTION2). The subspaces X and Y of (SYMBOL) inherit the subspace topology. In the following cases determine the interior, the closure, the boundary and the limit points of the subsets: 1, 2 and 3 *(For complete problem, including properly cited functions and symbols, pleas ...continues

Limit Points (Continuous Map)

Let f: X --> Y be a continuous map. Let A (SYMBOL) C. Show that, if (FUNCTION1) is closed, then (FUNCTION2). *(For complete problem, including proper citation of functions and symbols, please see attachment)