Question

Consider a closed nowhere dense set E ⊂ [0, 1]. consider a function g : [0,...

Consider a closed nowhere dense set E ⊂ [0, 1]. consider a function g : [0, 1] → R prove that if x is not an element of E, then g is continuous at x

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove: A nonempty subset C⊆R is closed if and only if there is a continuous function...
Prove: A nonempty subset C⊆R is closed if and only if there is a continuous function g:R→R such that C=g-1(0).
1. A function + : S × S → S for a set S is said...
1. A function + : S × S → S for a set S is said to provide an associative binary operation on S if r + (s + t) = (r + s) +t for all r, s, t ∈ S. Show that any associative binary operation + on a set S can have at most one “unit” element, i.e. an element u ∈ S such that (*) s + u = s = u + s for all...
Let E = {x + iy : x = 0, or x > 0, y =...
Let E = {x + iy : x = 0, or x > 0, y = sin(1/x)}. Prove that the set E is connected, but that is not path-connected or connected by trajectories and consider B = {z ∈ C : |z| = 1}. prove ( is easy to see it but how to prove it ) the following questions ¿is B open?¿is B closed?¿connected?¿compact?
A function f on a measurable subset E of Rd is measurable if for all a...
A function f on a measurable subset E of Rd is measurable if for all a in R, the set f-1([-∞,a)) = {x in E: f(x) < a} is measurable Prove that if f is continuous on Rd then f is measurable
We say that a set A is dense in a metric space (M,d) provided A bar...
We say that a set A is dense in a metric space (M,d) provided A bar = M. Show that if two continuous functions f, g :(M,d) tends to R on a dense set A, then they must agree on M
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected
Prove that the function f : R \ {−1} → R defined by f(x) = (1−x)...
Prove that the function f : R \ {−1} → R defined by f(x) = (1−x) /(1+x) is uniformly continuous on (0, ∞) but not uniformly continuous on (−1, 1).
Let g from R to R is a differentiable function, g(0)=1, g’(x)>=g(x) for all x>0 and...
Let g from R to R is a differentiable function, g(0)=1, g’(x)>=g(x) for all x>0 and g’(x)=<g(x) for all x<0. Proof that g(x)>=exp(x) for all x belong to R.
Consider the function ?:[0,1] → ℝ defined by ?(?) = 0 if ? ∈ [0,1] ∖...
Consider the function ?:[0,1] → ℝ defined by ?(?) = 0 if ? ∈ [0,1] ∖ ℚ and ?(?) = 1/? if ? = ?/? in lowest terms 1. Prove that ? is discontinuous at every ? ∈ ℚ ∩ [0,1]. 2. Prove that ? is continuous at every ? ∈ [0,1] ∖ ℚ
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements: A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R. Consider the relation ∼ on S given...