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Let $ (Z,W)$ be a compact Hausdorff space and $ \tilde X\subseteq Z$ an open subset of $ Z$ . Furthermore let $ h:(\tilde X, W_{|\tilde X}) \to (X, \mathcal T)$ be a homeomorphism. $ Y:=X \cup \{\infty\}$ How can I show that $ f: Z \to Y, f(x)=h(x)$ for $ x \in \tilde X$Read more

I have to prove this equation for a task. But, I was stuck here: Open image to know where I was stuckRead more

Let $ W = aI_{n\times n} + bJ_{n\times n}$ , where $ I$ is an identity matix, $ J$ is the matrix of all ones, $ a,b\in\mathbb{R}$ and a+b>0. Also, let $ A = \mathbf{P} – \mathbf{p}\mathbf{p}^{T}$ , where $ \mathbf{p} = (p_{1},\ldots,p_{n})^{T}$ and $ \mathbf{P} = \rm{diag}(\mathbf{p})$ with $ \sum_{i=1}^{n}p_i = 1$ and $Read more

and that our government needs to be more opaque? Also, Hillary’s 33,000 deleted govt emails are none of our damn business and Trump needs to release his taxes from when he was a private citizen? Yavan needs to be reported for promoting assassinations… once again.Read more

I am trying to prove that $ \omega_1$ is strongly inaccessible in $ L(r)$ for all $ r \subseteq \omega$ from the assumption that $ \omega_1$ is inaccessible to reals, i.e., that $ \omega_1^{L(r)} < \omega_1^V$ for all $ r \subseteq \omega$ . I have managed to prove that $ \omega_1^V$ is an uncountable regularRead more

http://www.independent.co.uk/news/trump-porn-star-payment-silence-stephanie-clifford-stormy-daniels-lawyer-michael-cohen-report-wsj-a8156761.html FAKERead more

Existence of one-way functions is a widely accepted conjecture in complexity theory. A function is one-way if it is computable in polynomial-time but not invertible in polynomial-time (this is different from the notion used in cryptography where average-case hardness is required). It seems we don not have any proof techniques that proves one-wayness. Let usRead more

Is it possible to carry out the following differential in Mathematica? $ $ d(1 \, dx) = d^2x$ $ I tried to write: Dt[1*Dt[x]] the result is: Dt[Dt[x]] instead of Dt^2[x]. Thank you so much for your willingness.Read more

I am trying to prove the graph-theoretic generalization of the following geometric observation: let $ \mathbb{P}$ be a finite set of distinct points in the Euclidean plane and $ card\left(CH\left(\mathbb{P}\right)\right)\ge4$ , where $ CH\left(\mathbb{P}\right)\subseteq\mathbb{P}$ denotes the set of points constituting to the convex hull of $ \mathbb{P}$ , then the following observation can be made:Read more

How do I prove: $ $ \frac{n}{\ln n}\not\sim\sqrt{n}$ $ It arises in my studies of the Goldbach conjecture.Read more