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Let $ \gamma$ be a limit ordinal with cofinality $ \kappa > \omega$ . Is there a stationary subset of $ \gamma$ (a subset of $ \gamma$ that meets every closed unbounded subset of $ \gamma$ ) of size $ \kappa$ ?Read more

Let $ \lambda\geq \omega_2$ be a regular cardinal and $ S\subset[\lambda]^\omega$ be a stationary set. I’m looking for a property of $ S$ , say “shootable”, such that there exists a forcing extension preserving $ \lambda, \omega_1$ as cardinals that shoots a club into $ S$ . I’ve encountered ad hoc examples, but I’d reallyRead more

We know every weakly open subset of an infinite-dimensional Banach vector space X is unbounded. Now, Read’s space $ R$ (an infinite-dimensional Banach space) has the property: there is $ ρ >0$ such that every weakly open subset of the unit ball of $ R$ has the diameter greater than or equal to $ ρ$Read more

Notations: Let $ K$ be a locally compact Hausdorff space and $ E$ be a real normed linear space. Recall that $ C_0(K,E)$ is the set of $ E$ -valued continuous functions $ f$ on $ K$ such that $ f$ vanishes at infinity. For any $ t\in K,$ let $ \psi_t$ be an evaluationRead more

Let $ A \subset B$ be an extension of integral domains and $ L=Q(B)$ , $ K=Q(A)$ the fraction fields. Let $ R \subset L$ be a $ K$ -algebra of finite type. Does there exist a finite type $ A$ -algebra $ R’$ with $ A \subset R’ \subset B$ and $ R \congRead more

I have an online sql server database in our company’s intranet. We made a small webapi using MS VS2015 as an interface to the database for certain applications. Now it may happen, that a user needs to access data offline (on commissioning e.g.). Is it possible to create a subset of the database locally, suchRead more

Given a positive integer $ n\in\mathbb{N}$ we define the zebra crossing associated with $ n$ to be the set $ $ Z_n = \{[2kn, 2kn+(n-1)] \cap \mathbb{N}: k\in\mathbb{N}\}.$ $ Is there an infinite set $ A\subseteq\mathbb{N}$ such that $ A\cap Z_n$ is finite for all positive integers $ n$ ?Read more

Let us consider the following set of $ \mathbb{C}^2$ : $ $ N=\{(|a|^2-4|b|^2,4a\overline{b}+b\overline{a});\;(a,b) \in \mathbb{C}^2\;\;\hbox{and}\;|a|^2+4|b|^2=1\} $ $ I want to prove that $ N$ is a convex set of $ \mathbb{C}^2$ . Thank youRead more

Consider the following variation of the coupon collector problem. We have $ n$ different coupons, from which coupons are being collected, equally likely, with replacement. We also have a collection $ C=\{S_1, S_2, \ldots, S_n\}$ of $ n$ proper subsets of $ [n]$ . For all indices $ i \in [n]$ , we have $Read more

The function work this way : 1. first of all you have to know that this function is part of a class and that the variable Set is an array of type generic. nElement is the size of all the subsets that you want. For exemple if you give it the value 3 the functionRead more