We introduce new techniques for studying the structure of partial k-trees. In particular, we show that the complements of partial k-trees provide an intuitively-appealing characterization of partial k-tree obstructions. We use this characterization to obtain a lower bound of 2 (k log k) on the number of obstructions, signi cantly improving the previously best-known bound of 2 ( p . Our techniqu...

‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

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C. Cawlfield, B. I. Eisenstein, I. Karliner, D. Kim, N. Lowrey, P. Naik, C. Sedlack, M. Selen, E. J. White, J. Wiss, M. R. Shepherd, D. Besson, T. K. Pedlar, D. Cronin-Hennessy, K. Y. Gao, D. T. Gong, J. Hietala, Y. Kubota, T. Klein, B. W. Lang, R. Poling, A. W. Scott, A. Smith, S. Dobbs, Z. Metreveli, K. K. Seth, A. Tomaradze, P. Zweber, J. Ernst, H. Severini, S. A. Dytman, W. Love, V. Savinov...