Intereting Posts

$A^2=A^*A$.Why $A$ is Hermitian matrix?
How to compute $\prod\limits^{\infty}_{n=2} \frac{n^3-1}{n^3+1}$
Regular polygons and Pythagoras
Why maximum/minimum of linear programming occurs at a vertex?
Be $f:\;(a,b)\rightarrow\mathbb{R}$ a continuous function. Suppose $c\in(a,b)$ …
Cross Ratio is positive real if four points on a circle
How do you find the solutions for $(4n+3)^2-48y^2=1$?
Book recommendation to prepare for geometry in the International Mathematical Olympiad
Derivation of Frey equation from FLT
Counterexample: $G \times K \cong H \times K \implies G \cong H$
Is the derivate on a closed subspace of $C^1$ is a continuous linear map?
Finding the first digit of $2015^{2015}$
Proving “The sum of n consecutive cubes is equal to the square of the sum of the first n numbers.”
Equal integral but only one of them converges absolutely .
Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

Let $X$ be an arbitrary topological space, and $U,V\subseteq X$ two subspaces of $X$ such that $U\cong V$ ($U$ and $V$ are homeomorphic) with respect the subspace topology of $X$. I know examples where $U$ is closed in $X$ and $V$ is not. Is there some conditions to guarantee the next statement:

If $U$ is closed in $X$, then $V$ es closed in $X$.

- half space is not homeomorphic to euclidean space
- Is there a function whose inverse is exactly the reciprocal of the function, that is $f^{-1} = \frac{1}{f}$?
- $KC$-spaces and $US$-spaces.
- Why formulate continuity in terms of pre-images instead of image?
- Example of a domain in R^3, with trivial first homology but nontrivial fundamental group
- Is a covering space of a completely regular space also completely regular

- Real life applications of Topology
- Proof that there is no Banach-Tarski paradox in $\Bbb R^2$ using finitely additive invariant set functions?
- For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $$
- Infimum is a continuous function, compact set
- Proving separability of the countable product of separable spaces using density.
- Question on problem: Equivalence of two metrics $\iff$ same convergent sequences
- Product of connected spaces - Proof
- Surgery link for lens spaces
- $|f(x)-f(y)|\le(x-y)^2$ without gaplessness
- Countable Chain Condition for separable spaces?

If $X$ is compact and Hausdorff, then a subspace is closed if and only if it is compact. Since compactness is a topological invariant, $X$ being compact Hausdorff ensures that if two subspaces are homeomorphic and one is closed, then so is the other.

- Relating the Künneth Formula to the Leray-Hirsch Theorem
- Differential of the inversion of Lie group
- A “number” with an infinite number of digits is a natural number?
- Cayley's Theorem – Questions on Proof Blueprint
- Why is a genus 1 curve smooth and is it still true for a non-zero genus one in general?
- Holder's inequality $ \sum_{i=1}^n |u_i v_i| \leq (\sum_{i=1}^n |u_i|^p )^{\frac{1}{p}}(\sum_{i=1}^n |v_i|^q )^\frac{1}{q} $
- Is showing $\lim_{z \to \infty} (1+\frac{1}{z})^z$ exists the same as $\lim_{n \to \infty} (1+1/n)^n$ exists
- $M$ is a flat $R$-module if and only if its character module, i.e. $\hom_{\mathbb{Z}}(M,\mathbb{Q/Z})$, is injective.
- Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
- Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2$
- Two finite abelian groups with the same number of elements of any order are isomorphic
- A closed form for $\int_0^\infty\frac{\ln(x+4)}{\sqrt{x\,(x+3)\,(x+4)}}dx$
- Prove ${\large\int}_0^1\frac{\ln(1+8x)}{x^{2/3}\,(1-x)^{2/3}\,(1+8x)^{1/3}}dx=\frac{\ln3}{\pi\sqrt3}\Gamma^3\!\left(\tfrac13\right)$
- Show that a positive operator on a complex Hilbert space is self-adjoint
- How to prove that compact subspaces of the Sorgenfrey line are countable?