R with Cofinite topology is not first countable space
Автор: Qais Ali Khan Lecturer Mathematics
Загружено: 2025-02-04
Просмотров: 158
In this lecture Qais Ali Khan proves that the set of real numbers along with cofinite topology is not first countable space. Qais Ali Khan completes this proof in three steps. In first step Qais Ali Khan writes about cofinite topology that the open sets in cofinite topology are the empty sets and the complements of finite sets. In fact the finite sets are closed in cofinite topology. In step two Qais Ali Khan assumes that the set of real numbers along with its cofinite topology is first countable space with the help of this assumption Qais Ali Khan got a statement and in step three this statement is proved wrong so the assumption that R with cofinite topology is first countable space is wrong because its resultant statement is wrong. In this way Qais Ali Khan proves that the set of real numbers along with its cofinite topology is not first countable space.
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