Intereting Posts

Is there an intuitionist (i.e., constructive) proof of the infinitude of primes?
Rotman introduction to theory of groups exercise
The constant of integration during integration by parts
formal proof from calulus
Minimization of Variational – Total Variation (TV) Deblurring
Transformation rule for a wedge product
How can I prove that all rational numbers are either terminating decimal or repeating decimal numerals?
dissection of rectangle into triangles of the same area
Roots of unity and a system of equations by Ramanujan
Direct proof that $(5/p)=1$ if $p\equiv 1\pmod{5}$.
For a Planar Graph, is it always possible to construct a set of cycle basis, with each and every edge Is shared by at most 2 cycle bases?
How to find $\sum_{k=1}^n k^k$?
Examples of applying L'Hôpitals rule ( correctly ) leading back to the same state?
Riemann tensor in terms of the metric tensor
How many non-isomorphic binary structures on the set of $n$ elements?

Which of the following subsets of $\mathbb{R}^2$ are compact?

- (a) $\left\{ (x, y) : xy = 1 \right\} $
- (b) $\left\{ (x, y) : x^{2/3} + y^{2/3} = 1 \right\}$
- (c) $\left\{(x, y) : x^2 + y^2 < 1\right\}$

clearly a and c are not compact. not sure about b

- A question from Arhangel'skii-Buzyakova
- Clopen subsets of a compact metric space
- Is it true that every normal countable topological space is metrizable?
- Transversal intersection.
- Why is Octahemioctahedron topologically a torus?
- Isomorphism isometries between finite subsets , implies isomorphism isometry between compact metric spaces

- Continuity based on restricted continuity of two subsets
- Build a topological manifold starting from a set.
- What does “relatively closed” mean?
- Why does Van Kampen Theorem fail for the Hawaiian earring space?
- Showing $H$ is a normal subgroup of $G$
- Why did we define the concept of continuity originally, and why it is defined the way it is?
- Every compact metric space is complete
- Help finding the fundamental group of $S^2 \cup \{xyz=0\}$
- Every subnet of $(x_d)_{d\in D}$ has a subnet which converges to $a$. Does $(x_d)_{d\in D}$ converge to $a$?
- Are all Infinite Simplicial Complexes non-compact?

Is the set bounded? For all $x\in\Bbb R$, $x^{2/3}\ge 0$, so if $x^{2/3}+y^{2/3}=1$, how big can $x$ and $y$ be?

Is it closed? That’s harder to answer rigorously, but a glance at the graph of the expression should give you a pretty good idea.

A subset of $\mathbb{R}^n$ is compact iff it is closed and bounded.

a) closed but unbounded so not compact.

b) closed and bounded.

c) Open set.

- Proposed proof of analysis result
- The value of a limit of a power series: $\lim\limits_{x\rightarrow +\infty} \sum_{k=1}^\infty (-1)^k \left(\frac{x}{k} \right)^k$
- Is the ''right limit'' function always right continuous?
- True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$
- What does the derivative of area with respect to length signify?
- Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
- Local maxima of Legendre polynomials
- Intersection of a properly nested sequence of convex sets , if nonempty and bounded , can never be open?
- Using Squeeze Theorem to show the following limits
- Prove that the real vector space consisting of all continuous, real-valued functions on the interval $$ is infinite-dimensional.
- Solution verification: Prove by induction that $a_1 = \sqrt{2} , a_{n+1} = \sqrt{2 + a_n} $ is increasing and bounded by $2$
- Is it possible to find out $x^2$ parabola and function from 3 given points?
- Prove that a holomorphic function with postive real part is constant
- fundamental period
- linear subspace of dual space