Newbetuts

Compare the topology of pointwise convergence with the vector topology in the space of the continuous scalar functions $C(I)$

Non-separable compact space

Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?

Find a continuous function $f:[1,\infty)\to\Bbb R $ such that $f(x) >0 $, $\int_1^\infty f(x)\,dx $ converges and $\int_1^\infty f(x)^2\,dx$ diverges

$X$ is homeomorphic to $X\times X$ (TIFR GS $2014$)

Separately continuous functions that are discontinuous at every point

Local homeomorphisms which are not covering map?

Necessity of completeness of the inner product space in Riesz representation theorem

Does a matrix $A$ of $\pm1$'s of order $11$ exist with $\det A >4000$?

Examples of pairewise independent but not independent continuous random variables

Maximal ideals and maximal subspaces of normed algebras

Example of two-dimensional non-abelian Lie algebra? [closed]

Is the rank of $AB$ always equal to the rank of $BA$?

Non-measurable set in product $\sigma$-algebra s.t. every section is measurable.

Give an example of a function $h$ that is discontinuous at every point of $[0,1]$, but with $|h|$ continuous on $[0,1]$

New posts in examples-counterexamples

Counterexamples in complex analysis

Weird measurable set

An ideal that is radical but not prime.

Reference request: product Borel $\sigma$-algebra of non-separable metric spaces

Example of nested closed balls with empty intersection?

Compare the topology of pointwise convergence with the vector topology in the space of the continuous scalar functions $C(I)$

Non-separable compact space

Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?

Find a continuous function $f:[1,\infty)\to\Bbb R $ such that $f(x) >0 $, $\int_1^\infty f(x)\,dx $ converges and $\int_1^\infty f(x)^2\,dx$ diverges

$X$ is homeomorphic to $X\times X$ (TIFR GS $2014$)

Separately continuous functions that are discontinuous at every point

Local homeomorphisms which are not covering map?

Necessity of completeness of the inner product space in Riesz representation theorem

Does a matrix $A$ of $\pm1$'s of order $11$ exist with $\det A >4000$?

Examples of pairewise independent but not independent continuous random variables

Maximal ideals and maximal subspaces of normed algebras

Example of two-dimensional non-abelian Lie algebra? [closed]

Is the rank of $AB$ always equal to the rank of $BA$?

Non-measurable set in product $\sigma$-algebra s.t. every section is measurable.

Give an example of a function $h$ that is discontinuous at every point of $[0,1]$, but with $|h|$ continuous on $[0,1]$