The possible number of islands on the sea |
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| Authors: | Pé ter Pá l Pach,Csaba Szabó |
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| Affiliation: | a Eötvös Loránd University, Department of Algebra and Number Theory, 1117 Budapest, Pázmány Péter sétány 1/c, Hungary
b Central European University, Hungary |
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| Abstract: | Let a height function f be a real valued function on R2. A connected subset of R2 is called an island, if there is a water level such that H is an island in the classical sense. We show that an island system is always laminar. Among others, in this paper we prove that the cardinality of a maximal laminar system is either countable or continuum. |
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| Keywords: | Maximal island system Countable Continuum |
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