Abstract
A Noetherian base B \mathcal {B} of a topological space X X is a base for the topology of X X which has the following property: If B 1 ⊂ B 2 ⊂ ⋯ {B_1} \subset {B_2} \subset \cdots is a nondecreasing sequence of elements of B \mathcal {B} , then { B n } n ∈ N {\left \{ {{B_n}} \right \}_{n \in {\mathbf {N}}}} is finite. In this article we give an example of a T 1 {T_1} topological space without a Noetherian base.
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