Abstract
Let X be a nonvoid set. A topology on X is a family τ⊂ P(X) of subsets which is closed under finite intersections and arbitrary unions. The pair (X,τ) is called a topological space, the elements ofτare called the open sets of the space. If τ1 and τ2 are topologies on X and τ1 ⊂ τ2 we say that τ2 is finer than τ1 or that τ1 is coarser than τ2. It exists in X a finest topology τ° = P(X) (called the discrete topology) and a coarsest one τ0 = {θ, X} (called the indiscrete topology). The elements of F={X \ G|G ∈ τ} are called the closed sets.
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© 1998 Springer Science+Business Media Dordrecht
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Cǎlugǎreanu, G., Hamburg, P. (1998). Rings of Continuous Functions. In: Exercises in Basic Ring Theory. Kluwer Texts in the Mathematical Sciences, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9004-4_16
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DOI: https://doi.org/10.1007/978-94-015-9004-4_16
Publisher Name: Springer, Dordrecht
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