When is a P-space weakly discretely generated?

Alas, Ofelia T.; Junqueira, Lúcia Renato; Wilson, Richard G.

doi:10.1016/j.topol.2013.10.001

Cited by 3 publications

(20 citation statements)

References 7 publications

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“…In the work [27] mentioned above, the authors show the following result: Theorem 2.0.2 (P. Komjáth, W. Weiss [27]). Let 𝑋 be a regular topological space with 𝑋 → (𝑡𝑜𝑝 𝜔 + 1) 1 𝜔 and 𝜒 (𝑋 ) < b. Then 𝑋 → (𝑡𝑜𝑝 𝛼) 1 𝜔 for all 𝛼 < 𝜔 1 .…”

Section: Partitions Of Topological Spacesmentioning

confidence: 99%

“…Let 𝑋 be a regular topological space with 𝑋 → (𝑡𝑜𝑝 𝜔 + 1) 1 𝜔 and 𝜒 (𝑋 ) < b. Then 𝑋 → (𝑡𝑜𝑝 𝛼) 1 𝜔 for all 𝛼 < 𝜔 1 . In the seminars organised by L. Junqueira a former student of hers R. Rodrigues presented the original proof of this theorem and we found a statement that we could not justify.…”

Section: Partitions Of Topological Spacesmentioning

confidence: 99%

“…Example 2.2.1. The real line ℝ is regular, has countable character and is such that ℝ → (𝑡𝑜𝑝 𝜔 + 1) 1 𝜔 .…”

Section: Rectifying the Original Theoremmentioning

confidence: 99%

“…Example 2.2.2. The Sorgenfrey line ℝ 𝑆 is regular, has countable character and is such that ℝ 𝑆 → (𝑡𝑜𝑝 𝜔 + 1) 1 𝜔 . As we can see, any hereditarily Lindelöf uncountable space is a space that satisfies part of the hypothesis from Theorem 2.0.2.…”

Section: Rectifying the Original Theoremmentioning

confidence: 99%

“…Example 2.2.3. The space 𝜔 1 + 1 with the order topology is regular, has character 𝜔 1 and 𝜔 1 + 1 → (𝑡𝑜𝑝 𝜔 + 1) 1 𝜔 .…”

Section: Rectifying the Original Theoremmentioning

confidence: 99%

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Covering properties,reflections in elementary submodels and partitions on topological spaces

Carvalho¹

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formation. I could not forget to thank my friends from all walks of life, those that have been with me since the school years, those I have met through my gaming hobbies and those that I have come to know through the academia, to the many memories and precious moments we shared. In particular, I would like to thank my friends Victor and Vinicius for our long conversations through Discord -sharing our worries and hopes -that helped me keep my sanity during this period. I would also like to thank all my teachers that helped me be the researcher I am today. In particular, I thank my Ph.D. advisor Lúcia for our talks, presentations and several ideas and suggestions made throughout my academic journey that helped in my formation and also to write my Ph.D. thesis. My gratitude also goes to Gabriel, not only for co-authoring my first -to be published -paper, but for also helping organizing our institute's set theoretic topology group, and helping me in my future academic endeavors. And finally an especially heartfelt thank you to my mother Maria Ines for her earnest concerns and hopes for me, so that she may know the importance of our conversations and her presence, which helped me, not only through the COVID-19 pandemic, but throughout my life. ResumoRodrigo Rey Carvalho. Propriedades de cobertura, reflexões em submodelos elementares e partições em espaços topológicos. Tese (Doutorado).

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