On the Cauchy integral theorem and Polish spaces
We prove that if a continuous function $f$ in an open subset $U\subset\mathbb{C}$ is analytic in $U\setminus X$, where $X\subset U$ is a Polish space having characteristic system $(k,n)\in\mathbb N_0\times\mathbb N$, then the complex line integral of $f$ along the boundary of any triangle in $U$ van...
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| Published in: | New Zealand journal of mathematics Vol. 56; pp. 45 - 51 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
14.08.2025
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| ISSN: | 1179-4984, 1179-4984 |
| Online Access: | Get full text |
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| Summary: | We prove that if a continuous function $f$ in an open subset $U\subset\mathbb{C}$ is analytic in $U\setminus X$, where $X\subset U$ is a Polish space having characteristic system $(k,n)\in\mathbb N_0\times\mathbb N$, then the complex line integral of $f$ along the boundary of any triangle in $U$ vanishes. |
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| ISSN: | 1179-4984 1179-4984 |
| DOI: | 10.53733/422 |