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1. CJM Online first

Elliott, George A.; Niu, Zhuang
 All Irrational Extended Rotation Algebras are AF Algebras Let $\theta\in[0, 1]$ be any irrational number. It is shown that the extended rotation algebra $\mathcal B_\theta$ introduced in a previous paper is always an AF algebra. Keywords:irrational rotation algebra, extended irrational rotation algebra, AF-embedding

2. CJM 2010 (vol 63 pp. 436)

Mine, Kotaro; Sakai, Katsuro
 Simplicial Complexes and Open Subsets of Non-Separable LF-Spaces Let $F$ be a non-separable LF-space homeomorphic to the direct sum $\sum_{n\in\mathbb{N}} \ell_2(\tau_n)$, where $\aleph_0 < \tau_1 < \tau_2 < \cdots$. It is proved that every open subset $U$ of $F$ is homeomorphic to the product $|K| \times F$ for some locally finite-dimensional simplicial complex $K$ such that every vertex $v \in K^{(0)}$ has the star $\operatorname{St}(v,K)$ with $\operatorname{card} \operatorname{St}(v,K)^{(0)} < \tau = \sup\tau_n$ (and $\operatorname{card} K^{(0)} \le \tau$), and, conversely, if $K$ is such a simplicial complex, then the product $|K| \times F$ can be embedded in $F$ as an open set, where $|K|$ is the polyhedron of $K$ with the metric topology. Keywords:LF-space, open set, simplicial complex, metric topology, locally finite-dimensional, star, small box product, ANR, $\ell_2(\tau)$, $\ell_2(\tau)$-manifold, open embedding, $\sum_{i\in\mathbb{N}}\ell_2(\tau_i)$Categories:57N20, 46A13, 46T05, 57N17, 57Q05, 57Q40

3. CJM 2008 (vol 60 pp. 961)

Abrescia, Silvia
 About the Defectivity of Certain Segre--Veronese Varieties We study the regularity of the higher secant varieties of $\PP^1\times \PP^n$, embedded with divisors of type $(d,2)$ and $(d,3)$. We produce, for the highest defective cases, a determinantal'' equation of the secant variety. As a corollary, we prove that the Veronese triple embedding of $\PP^n$ is not Grassmann defective. Keywords:Waring problem, Segre--Veronese embedding, secant variety, Grassmann defectivityCategories:14N15, 14N05, 14M12

4. CJM 2004 (vol 56 pp. 1068)

Steinbach, Anja; Van Maldeghem, Hendrik
 Regular Embeddings of Generalized Hexagons We classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type $\ssG_2$, $^3\ssD_4$ and $^6\ssD_4$ (and occurring in projective dimensions $5,6,7$), we find new examples in unbounded dimension related to the mixed groups of type $\ssG_2$. Keywords:Moufang generalized hexagons, embeddings, mixed hexagons, classical, hexagonsCategories:51E12, 51A45

5. CJM 1999 (vol 51 pp. 585)

Mansfield, R.; Movahedi-Lankarani, H.; Wells, R.
 Smooth Finite Dimensional Embeddings We give necessary and sufficient conditions for a norm-compact subset of a Hilbert space to admit a $C^1$ embedding into a finite dimensional Euclidean space. Using quasibundles, we prove a structure theorem saying that the stratum of $n$-dimensional points is contained in an $n$-dimensional $C^1$ submanifold of the ambient Hilbert space. This work sharpens and extends earlier results of G.~Glaeser on paratingents. As byproducts we obtain smoothing theorems for compact subsets of Hilbert space and disjunction theorems for locally compact subsets of Euclidean space. Keywords:tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embeddingCategories:57R99, 58A20