Let $F$ be a non-separable LF-space homeomorphic to the direct sum $sum_{ninmathbb{N}} ell_2( au_n)$, where $aleph_0 < au_1 < au_2 < cdots$.It is proved that every open subset $U$ of $F$ is homeomorphic to the product $|K| imes F$ for some locally finite-dimensional simplicial complex $K$ such that every vertex $v in K^{(0)}$ has the star $operatorname{St}(v,K)$ with $operatorname{card} operatorname{St}(v,K)^{(0)} < au = sup au_n$ (and $operatorname{card} K^{(0)} le au$), and, conversely, if $K$ is such a simplicial complex, then the product $|K| imes F$ can be embedded in $F$ as an open set, where $|K|$ is the polyhedron of $K$ with the metric topology.
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机译：假设$ F $是直接和$ sum_ {ninmathbb {N}} ell_2（au_n）$的不可分LF同胚，其中$ aleph_0 展开▼
