The definition of continuous function in topology
22 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it like
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22 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it like
Extension of continuous function on a closed subset of $mathbb {R}$ Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago
Can a discontinuous function have a continuous derivative? Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago
In fact, it turns out that every continuous function from a path connected space to $mathbb R$ is a quotient map Note that the closed map lemma cannot be generalised, for example
I was trying to formalize some things about string motion in physics so I could answer more general questions about it and then I got to a point as to see the limit written below. I then
are you talking about - a continuous function over a closed interval is uniformly continuous. then how should we generalize this over R
Existence of continuous sections of a continuous open surjection. Ask Question Asked 8 years, 9 months ago Modified 8 years, 9 months ago
Does continuous imply measurable? Ask Question Asked 7 years, 10 months ago Modified 7 years, 10 months ago
Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those
I think since we can apply Jensen''s inequality in the continuous case, we can still argue that the continuous case holds. Nevertheless, I cannot find any mention of Gibbs'' inequality in the