Geodesic
Not Every K1-Embedded Subspace is K0-Embedded
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 818-823

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All topological spaces under discussion are assumed to be Tychonoff.For any topological space X let τ(X) denote the topology of X. If X ᑕ Y then a function κ : τ(X) ⟶ τ(Y) is called an extender provided that κ(U) ∩ X = U for all U ∊ τ(X). In addition, X is said to be Kn-embedded in Y (cf. [3]) provided there is an extender κ : τ(X) ⟶ τ(Y) such that The extender κ is called a Kn -function (cf. [3]).Eric van Douwen has asked whether there is a space X with a subspace Z which is Ki -embedded but not K0 -embedded. The aim of this note is to answer this question. 
Mill, Jan van. Not Every K1-Embedded Subspace is K0-Embedded. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 818-823. doi: 10.4153/CJM-1979-076-7
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