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A proof that continuity of $f:X\to Y$ is equivalent to $\overline{f^{-1}(M)}\subset f^{-1}(\overline{M})$.

Is this alternative notion of continuity in metric spaces weaker than, or equivalent to the usual one?

Showing that $\lim_{h\rightarrow0}\max_{y\in[x,x+h]}f(y)=f(x)$

Continuity of function mapping connected set to connected set

iTunes wi-fi sync not working

Discontinuous functions that are continuous on every line in $\bf R^2$

Example of a function that has the Luzin $n$-property and is not absolutely continuous.

Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?

Is $\frac{x}{x-1}$ continuous on $(1,\infty)$? Prove it.

Is there a short proof for the Intermediate Value Theorem

Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?

Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?

Limit of the composition of two functions with f not necessarily being continuous.

Prove continuity for cubic root using epsilon-delta

Is this correct? Does no limit exist?

Question about the relation between integration and differentiation (From Calculus by Apostol)

New posts in continuity

A proof that continuity of $f:X\to Y$ is equivalent to $\overline{f^{-1}(M)}\subset f^{-1}(\overline{M})$.

Can we say that the point $(-3,2)$ is the local minimum?

Problem about continuous functions and the intermediate value theorem

Function is Continuous When Restricted to Closed Sets Which Cover the Space

Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $

Is this alternative notion of continuity in metric spaces weaker than, or equivalent to the usual one?

Showing that $\lim_{h\rightarrow0}\max_{y\in[x,x+h]}f(y)=f(x)$

Continuity of function mapping connected set to connected set

iTunes wi-fi sync not working

Discontinuous functions that are continuous on every line in $\bf R^2$

Example of a function that has the Luzin $n$-property and is not absolutely continuous.

Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?

Is $\frac{x}{x-1}$ continuous on $(1,\infty)$? Prove it.

Is there a short proof for the Intermediate Value Theorem

Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?

Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?

Limit of the composition of two functions with f not necessarily being continuous.

Prove continuity for cubic root using epsilon-delta

Is this correct? Does no limit exist?

Question about the relation between integration and differentiation (From Calculus by Apostol)