A Separately Continuous Function Not Somewhat Continuous
We construct a separately continuous function f : ℚ × ℚ → [0; 1] and a dense subset D ⊆ ℚ × ℚ such that f[D] is not dense in f[ℚ × ℚ], in other words, f is separately continuous and not somewhat (feebly) continuous.
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2022-03-01
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| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amsil-2021-0013 |
| _version_ | 1828369644515229696 |
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| author | Bielas Wojciech |
| author_facet | Bielas Wojciech |
| author_sort | Bielas Wojciech |
| collection | DOAJ |
| description | We construct a separately continuous function f : ℚ × ℚ → [0; 1] and a dense subset D ⊆ ℚ × ℚ such that f[D] is not dense in f[ℚ × ℚ], in other words, f is separately continuous and not somewhat (feebly) continuous. |
| first_indexed | 2024-04-14T06:27:29Z |
| format | Article |
| id | doaj.art-d440ac11fb3242ef8df7d13f4c64935e |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-04-14T06:27:29Z |
| publishDate | 2022-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-d440ac11fb3242ef8df7d13f4c64935e2022-12-22T02:07:45ZengSciendoAnnales Mathematicae Silesianae2391-42382022-03-01361262910.2478/amsil-2021-0013A Separately Continuous Function Not Somewhat ContinuousBielas Wojciech0Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007Katowice, PolandWe construct a separately continuous function f : ℚ × ℚ → [0; 1] and a dense subset D ⊆ ℚ × ℚ such that f[D] is not dense in f[ℚ × ℚ], in other words, f is separately continuous and not somewhat (feebly) continuous.https://doi.org/10.2478/amsil-2021-0013separate continuitysomewhat continuous function54c0854c3054g20 |
| spellingShingle | Bielas Wojciech A Separately Continuous Function Not Somewhat Continuous Annales Mathematicae Silesianae separate continuity somewhat continuous function 54c08 54c30 54g20 |
| title | A Separately Continuous Function Not Somewhat Continuous |
| title_full | A Separately Continuous Function Not Somewhat Continuous |
| title_fullStr | A Separately Continuous Function Not Somewhat Continuous |
| title_full_unstemmed | A Separately Continuous Function Not Somewhat Continuous |
| title_short | A Separately Continuous Function Not Somewhat Continuous |
| title_sort | separately continuous function not somewhat continuous |
| topic | separate continuity somewhat continuous function 54c08 54c30 54g20 |
| url | https://doi.org/10.2478/amsil-2021-0013 |
| work_keys_str_mv | AT bielaswojciech aseparatelycontinuousfunctionnotsomewhatcontinuous AT bielaswojciech separatelycontinuousfunctionnotsomewhatcontinuous |