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Keywords:
locally bounded densely continuous form; topology of pointwise convergence; cardinal function; weight; density; netweight; cellularity
locally bounded densely continuous form; topology of pointwise convergence; cardinal function; weight; density; netweight; cellularity
Summary:
We consider the space $D(X,Y)$ of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of $D(X,Y)$ and investigate the subspace $D^*(X)$ of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence $\tau _p$. The largest part of the paper is devoted to the study of various cardinal functions for $(D^*(X),\tau _p)$, in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, $\pi $-weight, $\pi $-character, netweight etc.
References:
[1] G. Beer: Topologies on Closed and Closed Convex Sets. Kluwer Academic Publishers, Dordrecht, 1993. MR 1269778 | Zbl 0792.54008
[2] C. Berge: Topological Spaces. Oliver and Boyd, Edinburgh, 1963. Zbl 0114.38602
[3] J. P. R. Christensen: Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings. Proceedings of the American Mathematical Society 86 (1982), 649–655. DOI 10.1090/S0002-9939-1982-0674099-0 | MR 0674099
[4] R. Engelking: General Topology. PWN - Polish Scientific Publishers, Warsaw, 1977. MR 0500780 | Zbl 0373.54002
[5] S. T. Hammer and R. A. McCoy: Spaces of densely continuous forms. Set-Valued Analysis 5 (1997), 247–266. DOI 10.1023/A:1008666504767 | MR 1486774
[6] ╝. Holá: Spaces of densely continuous forms, USCO and minimal USCO maps. Set-Valued Analysis 11 (2003), 133–151. DOI 10.1023/A:1022982924962 | MR 1966697
[7] ╝. Holá and R. A. McCoy: Cardinal invariants of the topology of uniform convergence on compact sets on the space of minimal USCO maps. Rocky Mountain Journal of Mathematics 37 (2007), 229–246. DOI 10.1216/rmjm/1181069328 | MR 2316446
[8] R. A. McCoy and I. Ntantu: Topological properties of spaces of continuous functions. Lecture Notes in Mathematics 1315, Springer-Verlag, Berlin, 1988. MR 0953314
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