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Examples-counterexamples
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Examples (trivial and non-trivial) of computable functions whose inverse is not computable
August 1st, 2022
computability
examples-counterexamples
computer-science
What is a typical example of the tensor product of modules failing to be left exact?
August 1st, 2022
examples-counterexamples
commutative-algebra
modules
Examples of non-finitely presented groups
August 1st, 2022
group-presentation
group-theory
examples-counterexamples
combinatorial-group-theory
Poset Infimum and Supremum
September 22nd, 2020
examples-counterexamples
order-theory
Examples of Separable Spaces that are not Second-Countable
August 1st, 2022
examples-counterexamples
general-topology
A Markov process which is not strong Markov process (follow up 2)
August 1st, 2022
examples-counterexamples
markov-process
stochastic-processes
Why doesn't the identity theorem for holomorphic functions work for real-differentiable functions?
August 1st, 2022
examples-counterexamples
complex-analysis
Image of a disconnected set is disconnected
August 1st, 2022
examples-counterexamples
connectedness
general-topology
Give an example of a bounded, non-convergent real sequence $(a_n)$ s.t. $a_n-a_{n-1}\rightarrow 0$
September 16th, 2020
analysis
sequences-and-series
examples-counterexamples
Is there a function that doesn't have a derivative?
August 1st, 2022
calculus
examples-counterexamples
derivatives
What's a very simple example of an equivariant map?
March 28th, 2021
examples-counterexamples
Is there a function that's continuous and has all directional derivatives as a linear function of direction, but still fails to be differentiable?
August 1st, 2022
real-analysis
multivariable-calculus
examples-counterexamples
Interesting examples of non-normal operators?
August 1st, 2022
examples-counterexamples
spectral-theory
linear-algebra
Why must a locally compact second countable Hausdorff space be second countable to imply paracompactness?
August 1st, 2022
general-topology
compactness
examples-counterexamples
second-countable
Example of non-Abelian group with 4, 5, or 6 elements of order 2
August 1st, 2022
abstract-algebra
examples-counterexamples
finite-groups
Regular space which is not Hausdorff
August 1st, 2022
examples-counterexamples
general-topology
Every compact subset must be closed?
August 1st, 2022
examples-counterexamples
general-topology
compactness
First countable + separable imply second countable?
August 1st, 2022
examples-counterexamples
separable-spaces
first-countable
general-topology
second-countable
Topological groups on the circle $S^1$
July 9th, 2020
circles
topological-groups
examples-counterexamples
group-theory
general-topology
Differentiability at a point does not imply differentiability on a neighbourhood. Do all similar implications fail?
August 1st, 2022
real-analysis
examples-counterexamples
$(0,1)\to\mathbb{R}^2$ injective, continuous, not a homeomorphism on the image
August 1st, 2022
examples-counterexamples
general-topology
A function continuous and bounded on a closed and bounded set but not uniformly continuous there
August 1st, 2022
real-analysis
continuity
examples-counterexamples
uniform-continuity
Example of Hausdorff and Second Countable Space that is Not Metrizable
August 1st, 2022
general-topology
examples-counterexamples
How to come up with a counter example in linear algebra
August 1st, 2022
linear-algebra
examples-counterexamples
Is every metric on the real line translation invariant.
August 1st, 2022
examples-counterexamples
metric-spaces
Counterexamples to Nakayama's Lemma if $M$ is not finitely generated
August 1st, 2022
modules
examples-counterexamples
commutative-algebra
ring-theory
abstract-algebra
Making Tychonoff Corkscrew in Counterexamples in Topology rigorous?
August 1st, 2022
examples-counterexamples
general-topology
iid variables, do they need to have the same mean and variance?
August 1st, 2022
probability-theory
examples-counterexamples
Is there a proof that is true for all cases except for exactly one case?
October 4th, 2020
big-list
proof-explanation
examples-counterexamples
Are these two equalities equivalent: $ABA=0$ and $BA=0$?
August 1st, 2022
linear-algebra
matrices
examples-counterexamples
matrix-equations
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