右有界非对称赋范空间中的局部compactness
Local compactness in right bounded asymmetric normed spaces
摘要：
我们刻画了有限维非对称赋范空间的右有界性质，以及这一性质与单位球的自然紧性（紧性和强紧性）之间的关系。与现有文献中的一些结果相比，我们表明并非所有右有界非对称范数都有紧闭球。我们还证明了有限维非对称赋范空间满足闭单位球是紧的，但不是强紧的，以这种方式关闭一个开放的问题上的拓扑结构的有限维非对称赋范空间。在正方向上，我们将证明有限维非对称赋范空间是强局部紧的当且仅当它是右有界的。
英文摘要：
We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some results found in the existing literature, we show that not all right bounded asymmetric norms have compact closed balls. We also prove that there are finite dimensional asymmetric normed spaces that satisfy that the closed unit ball is compact, but not strongly compact, closing in this way an open question on the topology of finite dimensional asymmetric normed spaces. In the positive direction, we will prove that a finite dimensional asymmetric normed space is strongly locally compact if and only if it is right bounded.
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