New posts in continuity

Continuity of composition of root and floor function

continuity radicals epsilon-delta ceiling-and-floor-functions

Image of a connected space under a continuous map is connected, proof

general-topology continuity proof-explanation connectedness

If every real valued continuous function on $X$ is uniformly continuous , then is every continuous function to any metric space uniformly continuous?

metric-spaces continuity uniform-continuity

Weaker Condition than Differentiability that Implies Continuity

real-analysis continuity

does the uniform continuity of $f$ implies uniform continuity of $f^2$ on $\mathbb{R}$?

Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?

real-analysis general-topology continuity

Does band-limited imply continuous?

fourier-analysis continuity harmonic-analysis

Difficulty in understanding a part in a proof from Stein and Shakarchi Fourier Analysis book.

integration polynomials continuity fourier-analysis fourier-series

Proof that a nonzero point is continuous for g(x)

calculus continuity proof-writing

Show that any two closed and bounded interval are homeomorphic in $\mathbb{R}$

general-topology continuity metric-spaces

Prove that $f_n(x)=\frac{x}{n}$, $n=1,2,\ldots$ does not converge uniformly on $\mathbb{R}$

calculus real-analysis proof-verification continuity

proof verification: $f(x) = 1/x$ is not uniformly continuous on the open interval (0,1).

real-analysis proof-verification continuity

Does continuity of a map $f$ imply: $f^{-1}$ maps subbasis onto subbasis?

general-topology continuity

Is $\frac{x^2-1}{x-1}$ continuous at $x=1$? [duplicate]

calculus limits continuity

Showing that $\Omega$ is of class $C^1$

real-analysis analysis integration continuity

Exercise about continuous functions

calculus real-analysis functions continuity

Study continuity of $f(x) = |x|$ for $x\in\Bbb R \setminus \Bbb Q$, $f(x) = \frac{qx}{q+1}$ for $x\in\Bbb Q$.

real-analysis calculus continuity

Why is a strictly monotonic mapping between intervals continuous?

real-analysis continuity monotone-functions

Nowhere continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f(f(x)) = (f(x))^2$

real-analysis functions continuity real-numbers

Function that is discontinuous only for integer fractions

analysis functions continuity