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New posts in continuity
Proof of continuity of Thomae Function at irrationals.
real-analysis
continuity
Why not include as a requirement that all functions must be continuous to be differentiable?
calculus
real-analysis
derivatives
continuity
definition
Why did mathematicians introduce the concept of uniform continuity?
real-analysis
general-topology
continuity
uniform-continuity
A continuous, nowhere differentiable but invertible function?
analysis
continuity
differential-topology
Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$
calculus
derivatives
continuity
examples-counterexamples
Theorem 18.1 of Munkres’ Topology
general-topology
continuity
proof-writing
alternative-proof
Continuity of the function $x\mapsto d(x,A)$ on a metric space
real-analysis
metric-spaces
continuity
Is $f(x) = 1/x$ over $[0.1 , 1]$ uniformly continuous but $1/x$ on $(0,1)$ is not?
real-analysis
analysis
continuity
uniform-continuity
Proof of "every convex function is continuous"
real-analysis
continuity
Show that a continuous function has a fixed point
real-analysis
analysis
continuity
fixed-point-theorems
fixed-points
Continuity and the Axiom of Choice
analysis
continuity
set-theory
axiom-of-choice
Counter example restriction of a function
real-analysis
continuity
No continuous function switches $\mathbb{Q}$ and the irrationals
real-analysis
functions
continuity
What functions can be made continuous by "mixing up their domain"?
real-analysis
general-topology
functions
continuity
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
real-analysis
continuity
functional-equations
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
general-topology
continuity
How to show that $f(x)=x^2$ is continuous at $x=1$? [closed]
calculus
continuity
A Topology such that the continuous functions are exactly the polynomials
general-topology
polynomials
continuity
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