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Motivation and examples for ramification
commutative-algebra
algebraic-number-theory
intuition
examples-counterexamples
motivation
Example of a continuous function with a discontinuous inverse
real-analysis
continuity
examples-counterexamples
inverse
If $V \times W$ with the product norm is complete, must $V$ and $W$ be complete?
functional-analysis
vector-spaces
banach-spaces
examples-counterexamples
normed-spaces
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
metric-spaces
examples-counterexamples
Does $\{f_ng_n\}\to fg$ uniformly?
real-analysis
sequences-and-series
general-topology
examples-counterexamples
uniform-convergence
A countale partially ordered set that has an uncountable number of maximal chains
set-theory
examples-counterexamples
Does $S^\bot+T^\bot = (S\cap T)^\bot$ hold in infinite-dimensional spaces?
linear-algebra
hilbert-spaces
examples-counterexamples
inner-products
Give an example of a simply ordered set without the least upper bound property.
general-topology
examples-counterexamples
order-theory
compactness
Does separability imply the Lindelöf property?
general-topology
examples-counterexamples
Is a product of derivatives still a derivative? [duplicate]
real-analysis
examples-counterexamples
A strong Hausdorff condition
general-topology
examples-counterexamples
separation-axioms
Find $f:C\to\mathbb{R}^2$ continuous and bijective but not open, $C\subset\mathbb{R} ^2$ is closed and connected
real-analysis
general-topology
examples-counterexamples
A congruence with the Euler's totient function and sum of divisors function
elementary-number-theory
prime-numbers
examples-counterexamples
totient-function
Examples of bi-implications ($\Leftrightarrow$) where the $\Rightarrow$ direction is used in the proof of the $\Leftarrow$ direction.
examples-counterexamples
big-list
If $R[x]$ and $R[[x]]$ are isomorphic, then are they isomorphic to $R$ as well? [duplicate]
polynomials
ring-theory
commutative-algebra
examples-counterexamples
formal-power-series
Infinite series involving $\sqrt{n}$
sequences-and-series
analysis
examples-counterexamples
Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?
abstract-algebra
field-theory
galois-theory
examples-counterexamples
Countably generated sigma-algebras
measure-theory
set-theory
examples-counterexamples
descriptive-set-theory
A locally injective but non globally injective function?
real-analysis
general-topology
examples-counterexamples
Limit point Compactness does not imply compactness counter-example
general-topology
examples-counterexamples
intuition
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