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Let $V,U,$ and $W$ be vector spaces, let $T∈L(V,U)$, and let $S∈L(U,W)$. Show that $N(ST)⊆N(T)$. Under what conditions does equality hold?

By ExtraProxies | Proxy Feed | Comments are Closed | 8 July, 2021 | 0

I think the problem that I was given by my school is wrong because $ \forall v \in N(T)$ , $ Tv=0$ , so we have $ STv=S(0)=0$ . Thus, $ v \in N(T)$ implies $ v \in N(ST)$ . Hence, $ N(T) \subseteq N(ST)$ . Am I right? Here, $ N(T), N(ST)$ means nullRead more

Using xcopy with folders with spaces

By ExtraProxies | Proxy User | Comments are Closed | 16 December, 2018 | 0

Using xcopy with the code below. I have read you can put double quotes around the source and destination folder so that the folders with spaces can be treated correctly as a directory. However, when I use quotes around the path it shows an error: Invalid number of parameters For /D %%K IN (“C:\This Folder”)Read more

Entab.c – Program that replaces string of blanks by the min # of spaces & tabs to achieve identical output

By ExtraProxies | Buying Proxies | Comments are Closed | 15 February, 2018 | 0

so you may have guessed from the title that this is Exercise 1-21 of K&R (2nd edition). I’ve seen someone else’s post about it but it doesn’t solve the problem the way my code does, and I wasn’t sure whether I was allowed to post my code as an answer and ask for feedback (itRead more

What is a standard name for this kind of unconditional bases in Banach spaces?

By ExtraProxies | Proxy Quality | Comments are Closed | 14 February, 2018 | 0

I am looking for a standard name (if it exists) for the following property of a Schauder basis $ (e_i)_{i=1}^\infty$ in a Banach space $ X$ : $ $ \|\sum_{i\in F}x_ie_i\|\le\|x\|$ $ for any $ x=\sum_{i=1}^\infty x_ie_i\in X$ and any finite subset $ F\subset\mathbb N$ . This condiion implies that the Schauder basis is unconditional.Read more

Good covers of complex-analytic spaces

By ExtraProxies | Proxy Quality | Comments are Closed | 11 February, 2018 | 0

There are several ways to construct good Cech covers of a smooth complex analytic space, by either using some little input from Riemannian geometry or complex analysis, for instance. What is a proof of existence of good Cech covers, that uses mostly the fact that a smooth complex analytic space $ X$ has an openRead more

Analytic cycles on complex-analytic spaces

By ExtraProxies | Proxy Quality | Comments are Closed | 10 February, 2018 | 0

If $ X$ is a proper smooth complex analytic space, one can define Chow groups of analytic cycles on $ X$ the usual way. We have a cycle map $ $ c^p_X: \text{CH}^p(X) \to \text{H}^{2p}_{D}(X,\mathbf{Z}(p))$ $ to Deligne cohomology of $ X$ . Is $ c^p_X$ an isomorphism? Is $ c^p_X\otimes\mathbf{Q}$ an isomorphism?Read more

How much is known about unstable homotopy of truncated projective spaces? – Reference request

By ExtraProxies | Proxy Quality | Comments are Closed | 6 February, 2018 | 0

I would like to know where about I can find the most updated results on the unstable groups $ \pi_{2k+1}P_{k+1}$ and $ \pi_{2k}P_k$ . I think there would be definitely computations Mahowald’s AMS memoir, but I presume there has been some work after this masterpiece! I also wonder how is known about the stable homotopyRead more

CW-complex of Eilenberg-MacLane spaces

By ExtraProxies | Proxy Quality | Comments are Closed | 1 February, 2018 | 0

What is the CW-complex of Eilenberg-MacLane space $ K(\mathbb{Z}_2,2)$ ? What is the CW-complex of Eilenberg-MacLane space $ K(\mathbb{Z}_n,d)$ ? What is the CW-complex of Eilenberg-MacLane space $ K(\mathbb{Z}_n\times \mathbb{Z}_m,d)$ ? For example, I like to know the number of cells in each dimensions, and the chain complex formed by those cells, so that oneRead more

bi-Lipschitz embeddings of compact metric spaces of fnite packing dimension into a Hilbert space

By ExtraProxies | Proxy Quality | Comments are Closed | 28 January, 2018 | 0

Problem. Does every compact metric space of finite packing dimension admit a bi-Lipschitz embedding into the Hilbert space $ \ell_2$ ? The packing dimension of a compact metric space $ (X,d)$ in the (finite or infinite) number $ $ Dim(X)=\limsup_{\varepsilon\to 0}\frac{\ln N_\varepsilon(X)}{\ln(1/\varepsilon)},$ $ where $ N_\varepsilon(X)$ is the cardinality of the smallest cover of $Read more

Paths in path component spaces

By ExtraProxies | Proxy Quality | Comments are Closed | 25 January, 2018 | 0

If $ X$ is a topological space, one can naturally view the set $ \pi_0(X)$ of path-components of $ X$ as a quotient space of $ X$ by collapsing each path-component to a point by a quotient map $ q:X\to \pi_0(X)$ . Of course, $ q$ is a homeomorphism if and only if $ X$Read more

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Private Proxies – Buy Cheap Private Elite USA Proxy + 50% Discount!
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