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Why are topological spaces interesting to study?

general-topology soft-question category-theory math-history asked Jul 31, 2013 at 11:34

math.stackexchange.com

30 votes

A Book for abstract Algebra

abstract-algebra reference-request self-learning book-recommendation asked Nov 18, 2012 at 9:53

math.stackexchange.com

25 votes

A polynomial with nowhere surjective derivative

abstract-algebra algebraic-geometry polynomials implicit-function-theorem asked Jul 22, 2019 at 18:25

math.stackexchange.com

23 votes

Existence of a certain functor $F:\mathrm{Grpd}\rightarrow\mathrm{Grp}$

group-theory category-theory groupoids asked May 1, 2013 at 23:05

math.stackexchange.com

23 votes

For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$

set-theory cardinals axiom-of-choice asked Jan 2, 2013 at 2:52

math.stackexchange.com

22 votes

Why is the second law of thermodynamics not symmetric with respect to time reversal?

thermodynamics entropy time-evolution time-reversal-symmetry arrow-of-time asked Oct 3, 2021 at 1:29

physics.stackexchange.com

20 votes

Do inequalities that hold for infinite sums hold for integrals too?

real-analysis measure-theory inequality integration integral-inequality asked Jan 7, 2013 at 8:23

math.stackexchange.com

20 votes

Monochromatic squares in a colored plane

discrete-mathematics coloring ramsey-theory asked Nov 22, 2012 at 18:05

math.stackexchange.com

18 votes

Construction of a Hausdorff space from a topological space

general-topology category-theory separation-axioms asked Aug 19, 2013 at 13:53

math.stackexchange.com

18 votes

Acceptance into graduate math programs

graduate-school graduate-admissions mathematics asked Feb 16, 2013 at 22:18

academia.stackexchange.com

Top Answers

Prove that odd perfect square is congruent to $1$ modulo $8$

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Is $\mathbb{Z}$ isomorphic to $\bigoplus_{p\in \mathbb{P}}\mathbb{Z}_p$?

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Prove $n\mid \phi(2^n-1)$

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limit question: $\lim\limits_{n\to \infty } \frac{n}{2^n}=0$

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Why don't we define "imaginary" numbers for every "impossibility"?

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please solve a 2013 th derivative question?

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Find all numbers $p$ such that all six numbers $p$, $p+2$, $p+6$, $p+8$, $p+12$, $p+14$ are primes

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Proof of $\arctan(x) = \arcsin(x/\sqrt{1+x^2})$

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Summation of odd power

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Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$

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Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$

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A field with finitely many elements

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Existance of multiple of $n$ with only 0 and 1 as it's digits

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How to solve $\ln x+x=1$

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alternating series test of $\sum(-1)^n\frac{\sqrt{n+1}-\sqrt{n}}{n}$

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For real numbers $x$ and $y$, show that $\frac{x^2 + y^2}{4} < e^{x+y-2} $

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Deriving Fermat's little theorem from $(a+1)^p\equiv a^p+1$ modulo $p$?

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Proving sum of $1/n^2$ is less than or equal to $2$

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Prove that the unit open ball in $\mathbb{R}^2$ cannot be expressed as a countable disjoint union of open rectangles.

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Examples illustrating the difference between closed and bounded sets.

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How to get the Galois group for $R/Q$

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Simplifying a dividing surd?

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Prime $p$ with $p^2+8$ prime

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Even cycles in a graph

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Simple proof; Show that $(4^n - 1)$ is divisible by 3 (Guided proof task)

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Prove that any group $G$ of order $p^2$ is abelian, where $p$ is a prime number

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Prove or disprove: There exists an integer $k\geq 4$ such that $2k^2 -5k+2$ is a prime number

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Finite group with condition that $H\subseteq K $ or $K\subseteq H$ on its subgroups

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Suppose there are two different spanning trees for a simple graph. Must they have an edge in common?

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Help with infinite sum

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