Intereting Posts

Basic Question on the Ideal-Variety Correspondence and Adjoint Functors
Find a formula for the nth Fibonacci Number
In this isosceles right angled triangle, prove that $\angle DAE = 45^{\circ}$
Calculate limit using Riemann integral
Prove that any palindrome with an even number of digits is divisible by 11.
If $A=AB-BA$, is $A$ nilpotent?
How to find roots of $f(z)=(a+yg(z))^2+g(z)^2=0$?
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
Geodesics of a Sphere in Cartesian Coordinates
Are exact representations of numbers in fractional bases unique?
$\sum \limits_{n=1}^{\infty}{a_n^2}$ converges $\implies \sum \limits_{n=1}^{\infty}{\dfrac{a_n}{n}}$
$|x| – |y| \leq |x-y|?$
Calculating an Angle from $2$ points in space
Localization at an element is intersection of localizations at primes not containing the element
Understanding the Proof of Dirac's Theorem Regarding Graph Connectivity

As the topic is there exist a homeomorphism between either pair of $(0, 1),(0,1],[0,1]$

- How to prove $D^n/S^{n-1}\cong S^n$?
- What does “relatively closed” mean?
- Topologically equivalent metric
- Is this a metric on R?
- Why is important for a manifold to have countable basis?
- The space obtained by identifying the antipodal points of a circle
- Do continuous linear functions between Banach spaces extend?
- Continuity of a function of product spaces
- Unit sphere in $\mathbb{R}^\infty$ is contractible?
- What does order topology over Ordinal numbers look like, and how does it work?

No two of the three spaces are homeomorphic. One way to see this is to note that $(0,1)$ has no non-cut points, $(0,1]$ has one non-cut point, and $[0,1]$ has two. (A non-cut point is one whose removal does **not** disconnect the space.) Another way to see that $[0,1]$ is not homeomorphic to either of the others is to note that $[0,1]$ is compact, and they are not. $(0,1)$ and $(0,1]$ can also be distinguished by the fact that the one-point compactification of $(0,1)$ is homeomorphic to the circle $S^1$, while that of $(0,1]$ is homeomorphic to $[0,1]$.

- Conditional probability independent of one variable
- Representation of compactly supported distribution
- Using 8×8 Binary Matrices as a hash
- General Steinitz exchange lemma
- Embeddings of finite groups into $\mathrm{GL}_n(\mathbb{Z})$
- Calculate the curvature of a parametrized curve
- Simple optimization trick
- weak subsolution
- Are there combinatorial games of finite order different from $1$ or $2$?
- inverse Laplace Transform: $ L^{-1} \{\log \frac{s^2 – a^2}{s^2} \}$.
- Integral domain with fraction field equal to $\mathbb{R}$
- Show $\int_0^\infty \frac{\cos a x-\cos b x}{\sinh \beta x}\frac{dx}{x}=\log\big( \frac{\cosh \frac{b\pi}{2 \beta}}{\cosh \frac{a\pi}{2\beta}}\big)$
- Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$
- An Example for a Graph with the Quaternion Group as Automorphism Group
- Combinatorial proof of $\Big|\prod\limits_{0 \leq i < j < N} (\zeta^j -\zeta^i)\Big| = \sqrt {N^N}$ for $\zeta \equiv \exp({2\pi i \over N})$