Newbetuts

$f, g:[a, b] \rightarrow [a, b] $ be any two continuous functions $(a, b \in \Bbb{R}) $ such that $\inf f(x) =\inf g(x) $

Prove $f: \mathbb{R}^d \to \mathbb{R}$ is continuous iff $f^{-1}(O)$ is open for any open set $O \subset \mathbb{R}$.

Uniformly continuous function acts almost like an Lipschitz function?

Explain why continuity along straight lines is not enough to conclude continuity

eventually constant maps

Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?

$f:X\to Y$ is continuous $\iff f^{-1}(A^) \subseteq (f^{-1}(A))^$

recursive sequence with continuous function

Two problems related to continuity of a metric from Munkres' topology book

$f(a)-f(b)$ is rational iff $f(a-b) $ is rational

Space of bounded and almost everywhere continuous function is complete?

Equivalence of continuity definitions [duplicate]

Calculating number of equivalence classes where two points are equivalent if they can be joined by a continuous path.

Is there a continuous version of the Borel-Cantelli lemma?

if the inverse images of all closed balls are closed, is $f$ continuous?

Are functions still continuous even with removable discontinuities?

Can a continuous function have discontinuities?

New posts in continuity

$f, g:[a, b] \rightarrow [a, b] $ be any two continuous functions $(a, b \in \Bbb{R}) $ such that $\inf f(x) =\inf g(x) $

Continuous linear functionals on the space $C[0,1]$ with topology of pointwise convergence

Avoid the planes - the geometry of grassmannians

Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space

Prove $f: \mathbb{R}^d \to \mathbb{R}$ is continuous iff $f^{-1}(O)$ is open for any open set $O \subset \mathbb{R}$.

Uniformly continuous function acts almost like an Lipschitz function?

Explain why continuity along straight lines is not enough to conclude continuity

eventually constant maps

Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?

$f:X\to Y$ is continuous $\iff f^{-1}(A^) \subseteq (f^{-1}(A))^$

recursive sequence with continuous function

Two problems related to continuity of a metric from Munkres' topology book

$f(a)-f(b)$ is rational iff $f(a-b) $ is rational

Space of bounded and almost everywhere continuous function is complete?

Equivalence of continuity definitions [duplicate]

Calculating number of equivalence classes where two points are equivalent if they can be joined by a continuous path.

Is there a continuous version of the Borel-Cantelli lemma?

if the inverse images of all closed balls are closed, is $f$ continuous?

Are functions still continuous even with removable discontinuities?

Can a continuous function have discontinuities?