Dense subspaces and addition theorems for paracompactness

作者：Arhangel'skii A V^*; Choban M M

来源：Topology and Its Applications, 2015, 185: 23-32.

DOI：10.1016/j.topol.2015.02.001

• Paracompact space
• Lindelof
• Metacompact
• Para-Lindelof
• Dense subspace
• Uniform base
• Strongly metacompact
• Souslin number

We establish that if a normal space X is the union of a finite collection of dense paracompact subspaces, then X is paracompact (Theorem 2.1), and prove that if a space X is the union of a finite family of dense paracompact subspaces, then X is metacompact (Theorem 2.2). A new class of strongly metacompact spaces is introduced and applied. In particular, it behaves nicely under taking the union of a finite collection of dense subspaces.

• 出版日期2015-5