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New posts in examples-counterexamples
Is there an easy example of a vector space which can not be endowed with the structure of a Banach space
banach-spaces
examples-counterexamples
normed-spaces
Example of a smooth 'step'-function that is constant below 0 and constant above 1
real-analysis
functions
examples-counterexamples
distribution-theory
analyticity
An undergraduate level example where the set of commutators is proper in the derived subgroup.
abstract-algebra
group-theory
examples-counterexamples
Is there a discontinuous function on the plane having partial derivatives of all orders?
real-analysis
multivariable-calculus
examples-counterexamples
partial-derivative
Does every number base have at least one "Baseless number"?
number-theory
diophantine-equations
examples-counterexamples
recreational-mathematics
number-systems
Complete space as a disjoint countable union of closed sets
general-topology
metric-spaces
examples-counterexamples
connectedness
baire-category
Examples of non-Riemann integrable functions that appear "in nature"?
calculus
soft-question
examples-counterexamples
Same homology but different fundamental group
algebraic-topology
manifolds
examples-counterexamples
homology-cohomology
fundamental-groups
An example of a noncommutative PID
ring-theory
modules
examples-counterexamples
If $f\tau$ is continuous for every path $\tau$ in $X$, is $f:X\rightarrow Y$ continuous?
general-topology
examples-counterexamples
A derivative which is not Lebesgue integrable on any interval?
real-analysis
derivatives
examples-counterexamples
lebesgue-integral
What does a Godel sentence actually look like?
logic
examples-counterexamples
incompleteness
Definition of time-constructible function
computational-complexity
examples-counterexamples
Construct an example of set $A$ for which $A+A=A $ but $0∉cl(A)$
convex-analysis
examples-counterexamples
Does there exist a ring which is not a principal ideal ring and which has exactly six different ideals?
abstract-algebra
ring-theory
ideals
examples-counterexamples
principal-ideal-domains
Is there a dense subset of [0,1] of measure 1/2 whose complement is also dense?
measure-theory
examples-counterexamples
Maximal ideals in $C^\infty(\mathbb{R})$
abstract-algebra
functions
ring-theory
examples-counterexamples
ideals
If $f$ preserves identity and inverses, is it necessarily a group homomorphism?
group-theory
examples-counterexamples
inverse
group-homomorphism
A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
elementary-set-theory
examples-counterexamples
order-theory
Difficulty in finding a counterexample
real-analysis
limits
continuity
examples-counterexamples
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