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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
A Sequel To “A Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa
A Sequel To “A Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa
Faculty Publications
We consider a topological space ⟨𝑋, 𝜏 (ℱ)⟩, where 𝑋 = {𝑝 ∗} ∪ [𝜔 Å~ 𝜔] and ℱ ⊆ 𝜔𝜔. Each point in 𝜔 Å~ 𝜔 is isolated and a neighborhood of 𝑝∗ has the form {𝑝∗}∪{⟨𝑖, 𝑗⟩ : 𝑖 ≥ 𝑛, 𝑗 ≥ 𝑓(𝑖)} for some 𝑛 ∈ 𝜔 and 𝑓 ∈ ℱ. We show that there are subsets ℱ and 𝒢 of 𝜔𝜔 such that ℱ is not bounded, 𝒢 is bounded, yet ⟨𝑋, 𝜏 (ℱ)⟩ and ⟨𝑋, 𝜏 (𝒢)⟩ are homeomorphic. This answers a question of the second author posed in A space topologized by functions …
A Space Topologized By Functions From Omega To Omega, Akira Iwasa
A Space Topologized By Functions From Omega To Omega, Akira Iwasa
Faculty Publications
No abstract provided.
Covering Properties And Cohen Forcing, Akira Iwasa
Covering Properties And Cohen Forcing, Akira Iwasa
Faculty Publications
We will show that adding Cohen reals preserves the covering property that every open cover has a σ-P Q refinement and deduce that adding Cohen reals preserves covering properties such as paracompactness, subparacompactness and screenability.
Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa
Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa
Faculty Publications
We discuss when a subspace of ωω is paracompact in some forcing extension.