Intereting Posts

There exist a function such that $f\circ f(x)=e^x$?
Why does an argument similiar to 0.999…=1 show 999…=-1?
At least one monochromatic triangle from $p_n=\lfloor{en!}\rfloor+1$ points
Quaternion group as an extension
Prove $\sum_{k=1}^{\infty} \frac{\sin(kx)}{k} $ converges
Injective and Surjective Functions
Equal slicing of my spherical cake
How many numbers between $100$ and $900$ have sum of their digits equal to $15$?
Overview of basic results on cardinal arithmetic
When is the integral closure of a local ring also a local ring?
Construct a compact set of real numbers whose limit points form a countable set.
List of matrix properties which are preserved after a change of basis
Prove $\sin a=\int_{-\infty}^{\infty}\cos(ax^2)\frac{\sinh(2ax)}{\sinh(\pi x)} \operatorname dx$
If $ -3\left(x-\lfloor x \rfloor \right)^2+2(x-\lfloor x \rfloor )+a^2=0$ has no integral solution, then $a$ is
Magnitude of differentiable complex function $f(z)$

I am looking for a reference (not proof) to the following theorem:

If $X$ is a compact and locally connected topological space, Y is a Hausdorff topological space, $f:X\to Y$ is continuous and $f(X)=Y$, then $Y$ is locally connected.

I found reference in Kuratowski, Topology II for the case where $X$ is metrizable. Any one knows about any reference to this case?

- Show the given space is uncountable.
- Spaces where all compact subsets are closed
- Properties of compact set: non-empty intersection of any system of closed subsets with finite intersection property
- Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?
- A sequentially compact subset of $\Bbb R^n$ is closed and bounded
- Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.

- If the graph of a function $f: A \rightarrow \mathbb R$ is compact, is $f$ continuous where $A$ is a compact metric space?
- How to prove that a topological space is connected iff it has exactly two clopen subsets?
- Does path-connected imply simple path-connected?
- Transient diffusion with compact support throughout (not just initially)
- Finer topologies on a compact Hausdorff space
- What's going on with “compact implies sequentially compact”?
- Stone–Čech compactification of $\mathbb{N}, \mathbb{Q}$ and $\mathbb{R}$
- $f$ continuous iff $\operatorname{graph}(f)$ is compact
- The complement of every countable set in the plane is path connected
- Complement of a totally disconnected compact subset of the plane

- Writing a GCD of two numbers as a linear combination
- On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
- If $M$ is an artinian module and $f : M\to M$ is an injective homomorphism, then $f$ is surjective.
- Is there any trivial reason for $2$ is irreducible in $\mathbb{Z},\omega=e^{\frac{2\pi i}{23}}$?
- Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
- The dense topology
- Taking the second derivative of a parametric curve
- Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
- Hard planar graph problem
- Evaluating a trigonometric product $\prod_{n=1}^{\infty}\cos^2\left(\frac{1}{n^2}\right)$
- Maximal submodule in a finitely generated module over a ring
- Is the Nested Radical Constant rational or irrational?
- Gamma Infinite Summation $\sum_{n=0}^{\infty}\frac{\Gamma(n+s)}{n!}=0$
- Another way to go about proving the limit of Fibonacci's sequence quotient.
- Is there an alternative proof for periodic expansion of decimal fraction?