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Jan
2
revised Proof of $f \in C_C(X)$ where $X$ is a metric space implies $f$ is uniformly continuous
added 64 characters in body
Jan
2
comment Proof of $f \in C_C(X)$ where $X$ is a metric space implies $f$ is uniformly continuous
@Johan For a continuous function $f$ I have that for an $\varepsilon$ I can find a $\delta$ such that $f(B(x, \delta)) \subset B(f(x), \varepsilon)$. Above I have chosen $\delta_i$ such that $f(B(x_i, \delta_i)) \subset B(f(x_i), \varepsilon)$. I also have $x,y \in B(x_i,\delta_i)$ so $f(x), f(y) \in f(B(x_i,\delta_i)) \subset B(f(x_i), \varepsilon)$ and therefore $|f(x) - f(y)| < 2 \varepsilon$. Can you point out my thinko more explicitly please? I still don't see it, thank you.
Jan
2
revised Proof of $f \in C_C(X)$ where $X$ is a metric space implies $f$ is uniformly continuous
added 4 characters in body
Jan
2
accepted Proof of $f \in C_C(X)$ where $X$ is a metric space implies $f$ is uniformly continuous
Jan
2
comment Proof of $f \in C_C(X)$ where $X$ is a metric space implies $f$ is uniformly continuous
@t.b. That was a "thinko", not a typo. Yes, of course it's less than $2 \varepsilon$. Thank you!
Jan
2
asked Proof of $f \in C_C(X)$ where $X$ is a metric space implies $f$ is uniformly continuous
Jan
1
awarded  Disciplined
Jan
1
accepted $H_1(X,A) = 0 \iff H_1(A) \rightarrow H_1(X)$ surjective and $X_i$ contains no more than one path-component of $A$
Jan
1
accepted $H_1(\mathbb{R}, \mathbb{Q})$ is free abelian
Jan
1
accepted Equivalent identification to get the projective plane?
Jan
1
accepted Homology of disjoint union is direct sum of homologies
Jan
1
accepted Proof of another Hatcher exercise: homotopy equivalence induces bijection (part II)
Jan
1
comment An inequality about maximal function
What's the maximal function of $f$?
Dec
31
comment Clarifying the definition of “unstable”
@J.M. Nice, thanks : ) And thanks for the vote, I assume it was you.
Dec
31
comment Clarifying the definition of “unstable”
@J.M. Do you approve of my edit above?
Dec
31
revised Clarifying the definition of “unstable”
added 303 characters in body
Dec
31
comment Clarifying the definition of “unstable”
@J.M. Hmmm. I just re-read the question and it reads to me as "Are there any algorithms where the error of the algorithm is insignificant with respect to the method itself?" But the algorithm is the method itself. Am I confused?
Dec
31
comment Clarifying the definition of “unstable”
@J.M. True, I forgot about ill-conditioned problems. But I've not heard of forward and backward stability I think. Yet I don't think this falsifies my answer.
Dec
31
comment Set Notation Excercise
Yes, exactly : )
Dec
31
answered Set Notation Excercise