query: Continuity of a function
positive_passages.docid: 22303
positive_passages.text: How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
negative_passages.docid: 18222
negative_passages.text: Set of continuity points of a real function
negative_passages.docid: 118048
negative_passages.text: Can a function with just one point in its domain be continuous?
negative_passages.docid: 50725
negative_passages.text: Inverse of function is continuous or not?
negative_passages.docid: 143618
negative_passages.text: If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
negative_passages.docid: 12523
negative_passages.text: Supremum of a Continuous Function is Continuous
negative_passages.docid: 120947
negative_passages.text: continuous real-valued function
negative_passages.docid: 65346
negative_passages.text: Characterisation of uniformly continuous function
negative_passages.docid: 17234
negative_passages.text: Show that a continuous function has a fixed point
negative_passages.docid: 142459
negative_passages.text: Continuity of a Function in Terms of Closure and Interior
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable
negative_passages.docid: 125745
negative_passages.text: continuity of power series
negative_passages.docid: 150554
negative_passages.text: proof that $f'$ is continuous at $a$
negative_passages.docid: 132013
negative_passages.text: How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
negative_passages.docid: 146929
negative_passages.text: smooth functions or continuous
negative_passages.docid: 133696
negative_passages.text: Example of a function continuous at only one point.
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous