Intereting Posts

Continuity of a function of product spaces
Existence of Homomorphism so that Diagram Commutes
Differentiate $\sin \sqrt{x^2+1} $with respect to $x$?
Image of open donut under $\phi=z+\frac{1}{z}$
Unpacking the Diagonal Lemma
proof using the mathematical induction
Dimension of the total ring of fractions of a reduced ring.
$\int dx \; f(\sqrt{x^2+a^2})$ by substitution $u=\sqrt{x^2+a^2}$
Asymmetric Hessian matrix
Probability of asymmetric random walk returning to the origin
How to generate random symmetric positive definite matrices using MATLAB?
Why characters are continuous
Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power
Integer solutions to nonlinear system of equations $(x+1)^2+y^2 = (x+2)^2+z^2$ and $(x+2)^2+z^2 = (x+3)^2+w^2$
How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt{2+\sqrt{3+\dotsb+\sqrtn}}$?

The connected sum of closed surfaces (2-manifolds) is defined by removing a disk from each and gluing the exposed edges together.

When defining the connected sum of surfaces with boundary, is the boundary of each surface allowed to touch its removed disk?

By my intuition it seems like a bad idea to allow that, because that might lead to “not nice” behaviours. But I can’t really think of anything in the formal definition that could forbid it – removing an open disk doesn’t prevent the disk from touching the surface boundary.

- The degree of a polynomial which also has negative exponents.
- Is $1234567891011121314151617181920212223…$ an integer?
- Is the empty set linearly independent or linearly dependent?
- Understanding of extension fields with Kronecker's thorem
- What is Abstract Algebra essentially?
- Borel Measures: Atoms (Summary)

- What is the most rigorous definition of a matrix?
- How exactly can't $\delta$ depend on $x$ in the definition of uniform continuity?
- The formula for a distance between two point on Riemannian manifold
- An open subset of a manifold is a manifold
- Is the function $f(x)=x$ on $\{\pm\frac1n:n\in\Bbb N\}$ differentiable at $0$?
- Equivalent form of definition of manifolds.
- $M \times N$ orientable if and only if $M, N$ orientable
- What are central automorphisms used for?
- Show that the set $M$ is not an Embedded submanifold
- Product of spaces is a manifold with boundary. What can be said about the spaces themselves?

- Is there a polynomial-time algorithm to find a prime larger than $n$?
- Prove that $Ω$ has no accumulation point
- What are some interesting calculus facts your calculus teachers didn't teach you?
- Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
- On the convexity of element-wise norm 1 of the inverse
- Avoiding proof by induction
- $7$ points inside a circle at equal distances
- A theorem about Cesàro mean, related to Stolz-Cesàro theorem
- Asymptotic behaviour of $\sum_{p\leq x} \frac{1}{p^2}$
- How many absolute values are there?
- Uncorrelating random variables.
- Ultrafilter Lemma and Alexander subbase theorem
- Abstract algebra book recommendations for beginners.
- Let $G$ a group of order $6$. Prove that $G \cong \Bbb Z /6 \Bbb Z$ or $G \cong S_3$.
- Why is Erdős–Szekeres theorem sharp?