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Physical Sciences and Mathematics Commons™

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Faculty Publications

Applied Mathematics

University of South Carolina

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Full-Text Articles in Physical Sciences and Mathematics

Preservation Of A Convergence Of A Sequence To A Set, Akira Iwasa, Masaru Kada, Shizuo Kamo Jan 2014

Preservation Of A Convergence Of A Sequence To A Set, Akira Iwasa, Masaru Kada, Shizuo Kamo

Faculty Publications

We say that a sequence of points converges to a set if every open set containing the set contains all but finitely many terms of the sequence. We investigate preservation of convergence of a sequence to a set in forcing extensions.

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A Sequel To β€œA Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa Dec 2010

A Sequel To β€œA Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa

Faculty Publications

We consider a topological space βŸ¨π‘‹, 𝜏 (β„±)⟩, where 𝑋 = {𝑝 βˆ—} βˆͺ [πœ” Γ…~ πœ”] and β„± βŠ† πœ”πœ”. Each point in πœ” Γ…~ πœ” is isolated and a neighborhood of π‘βˆ— has the form {π‘βˆ—}βˆͺ{βŸ¨π‘–, π‘—βŸ© : 𝑖 β‰₯ 𝑛, 𝑗 β‰₯ 𝑓(𝑖)} for some 𝑛 ∈ πœ” and 𝑓 ∈ β„±. We show that there are subsets β„± and 𝒒 of πœ”πœ” such that β„± is not bounded, 𝒒 is bounded, yet βŸ¨π‘‹, 𝜏 (β„±)⟩ and βŸ¨π‘‹, 𝜏 (𝒒)⟩ are homeomorphic. This answers a question of the second author posed in A space topologized by functions …

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A Space Topologized By Functions From Omega To Omega, Akira Iwasa Jun 2009

A Space Topologized By Functions From Omega To Omega, Akira Iwasa

Faculty Publications

No abstract provided.

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Covering Properties And Cohen Forcing, Akira Iwasa Jan 2007

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 Οƒ-P Q refinement and deduce that adding Cohen reals preserves covering properties such as paracompactness, subparacompactness and screenability.

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Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa Jan 2006

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.

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