کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661017 | 1633120 | 2008 | 9 صفحه PDF | دانلود رایگان |
Some new results on relationships between cardinal invariants in compacta are obtained. We establish that every non-separable compactum admits a continuous mapping onto a compactum of the weight ω1 that has a dense non-separable monolithic subspace (Lemma 1). Lemma 1 easily implies Shapirovskij's theorem that every compactum of countable tightness and of precaliber ω1 is separable. The lemma also opens the road to some generalizations of this statement and to other results. We also obtain new results on the structure of monolithic compacta and of homogeneous compacta. In particular, a new class of shell-homogeneous compacta is introduced and studied. One of the main results here is Theorem 31 which provides a generous sufficient condition for a homogeneous monolithic compactum to be first countable. Many intriguing open questions are formulated.
Journal: Topology and its Applications - Volume 155, Issues 17–18, 15 October 2008, Pages 2128-2136