Intereting Posts

Equation of a curve
Prove that if f in $C(X \times Y)$ then there exists functions.
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
Are there ideals in $M_n(P)$ that are not of the form $M_n(I)$?
Factoring with fractional exponents
elementary ways to show $\zeta(-1) = -1/12$
Infinite Series $\sum\limits_{k=1}^{\infty}\frac{k^n}{k!}$
The derivative of $x!$ and its continuity
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $$
Finitely presented Group with less relations than Generators.
There exist $x_{1},x_{2},\cdots,x_{k}$ such two inequality $|x_{1}+x_{2}+\cdots+x_{k}|\ge 1$
Proof by Induction:
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
General Proof for the triangle inequality
This one weird trick integrates fractals. But does it deliver the correct results?

It is well-known that the generators of the zeroth singular homology group $H_0(X)$ of a space $X$ correspond to the path components of $X$.

I have recently learned that for Čech homology the corresponding statement would be that $\check{H}_0(X)$ is generated by the quasicomponents of $X$. This leads me to my question:

Are there any homology theories (in a broad sense; i.e. not necessarily satisfying all of Eilenberg-Steenrod axioms) being used such that the zeroth homology of a space is generated by its connected components?

- What is the homotopy type of the affine space in the Zariski topology..?
- Seifert matrices and Arf invariant — Cinquefoil knot
- When a covering map is finite and connected, there exists a loop none of whose lifts is a loop.
- Homotopy functions
- Applications of algebra and/or topology to stochastic (or Markov) processes
- Covering space is a fiber bundle

- Calculate the cohomology group of $U(n)$ by spectral sequence.
- k-Cells are Connected
- Are all paths with the same endpoints homotopic in a simply connected region?
- Why does zero derivative imply a function is locally constant?
- Alternative definition of covering spaces.
- Two CW complexes with isomorphic homotopy groups and homology, yet not homotopy equivalent
- Computing the homology groups.
- Is homology with coefficients in a field isomorphic to cohomology?
- Prove that the set of $n$-by-$n$ real matrices with positive determinant is connected
- Spaces with equal homotopy groups but different homology groups?

- Monotonicity of function of two variables
- Why adjoining non-Archimedean element doesn't work as calculus foundation?
- Smoothness and decay property of Fourier transformation
- Counterexample Math Books
- Closed form of $ x^3\sum_{k=0}^{\infty} \frac{(-x^4)^k}{(4k+3)(1+2k)!} $
- Field bigger than $\mathbb{R}$
- Integral $\int_0^1 \frac{\ln (2-x)}{2-x^2} \, dx$
- Calculating prime numbers
- Trigonometry problem on product of trig functions.
- Existence of additive transformation of random variables
- What is the dot product and why do we need it?
- Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
- Tensor Book Recommendation Request
- Limiting distribution.
- Find All $x$ values where $f(x)$ is Perfect Square