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New posts in examples-counterexamples
An example of a non-paracompact topological space
general-topology
examples-counterexamples
paracompactness
If $f:[a,b]\to \mathbb{R}$ satisfies $|f'(x)|<1, \forall x\in [a,b]$, is $f$ necessarily a contraction?
real-analysis
examples-counterexamples
Concrete examples of group actions.
group-theory
examples-counterexamples
group-actions
What are some interesting counterexamples given by finite topological spaces?
general-topology
examples-counterexamples
Counterexample for graph isomorphism using eigenvalue multiplicity (connected graphs)
graph-theory
examples-counterexamples
Two claims about compositorials
elementary-number-theory
prime-numbers
examples-counterexamples
products
Pretty conjecture $x^{\left(\frac{y}{x}\right)^n}+y^{\left(\frac{x}{y}\right)^n}\leq 1$
derivatives
inequality
examples-counterexamples
exponentiation
conjectures
Example of a function in $L^2(\mathbb{R})$ with derivative not in $L^2(\mathbb{R})$.
functional-analysis
derivatives
lebesgue-integral
examples-counterexamples
Is total boundedness a topological property?
general-topology
metric-spaces
examples-counterexamples
Does the Laplace transform biject?
functions
examples-counterexamples
laplace-transform
Why differentiability implies continuity, but continuity does not imply differentiability?
real-analysis
derivatives
continuity
examples-counterexamples
Extending Herstein's Challenging Exercise to Modules
abstract-algebra
group-theory
commutative-algebra
examples-counterexamples
sigmoid $\circ$ sigmoid = sigmoid?
functions
examples-counterexamples
function-and-relation-composition
How big can $U\subset\mathbb{C}$ be if there exists a non-constant holomorphic $f\colon U\to\mathbb{C}$ with $2f(2z)=f(z)+f(z+1)?$
complex-analysis
examples-counterexamples
Counterexample to Tonelli's theorem
real-analysis
integration
examples-counterexamples
fubini-tonelli-theorems
Non-examples for the Kato-Rellich Theorem
linear-algebra
functional-analysis
partial-differential-equations
hilbert-spaces
examples-counterexamples
Associative, non-commutative, nontrivial operation on the real numbers
examples-counterexamples
binary-operations
associativity
Universal property characterizing $\Bbb R$
category-theory
examples-counterexamples
Does there exist a function $f: \mathbb{R} \to \mathbb{R}$ that is differentiable only at $0$ and at $\frac{1}{n}$, $n \in \mathbb{N}$?
calculus
real-analysis
derivatives
examples-counterexamples
Examples of bijections from $\mathbb Z\to\mathbb Z$ such that their sum is a bijection?
functions
elementary-set-theory
examples-counterexamples
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