TY - JOUR

T1 - Irreducible quotient maps from locally compact separable metric spaces

AU - Lazar, A. J.

AU - Somerset, D. W.B.

N1 - Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - Let X be a Hausdorff quotient of a standard space (that is of a locally compact separable metric space). It is shown that the following are equivalent: (i) X is the image of an irreducible quotient map from a standard space; (ii) X has a sequentially dense subset satisfying two technical conditions involving double sequences; (iii) whenever q:Y→X is a quotient map from a standard space Y, the restriction q⁎|V is an irreducible quotient map from V onto X (where q⁎:Y⁎→X is the pure quotient derived from q, and V is the closure of the set of singleton fibres of Y⁎). The proof uses extensions of the theorems of Whyburn and Zarikian from compact to locally compact standard spaces. The results are new even for quotients of locally compact subsets of the real line.

AB - Let X be a Hausdorff quotient of a standard space (that is of a locally compact separable metric space). It is shown that the following are equivalent: (i) X is the image of an irreducible quotient map from a standard space; (ii) X has a sequentially dense subset satisfying two technical conditions involving double sequences; (iii) whenever q:Y→X is a quotient map from a standard space Y, the restriction q⁎|V is an irreducible quotient map from V onto X (where q⁎:Y⁎→X is the pure quotient derived from q, and V is the closure of the set of singleton fibres of Y⁎). The proof uses extensions of the theorems of Whyburn and Zarikian from compact to locally compact standard spaces. The results are new even for quotients of locally compact subsets of the real line.

KW - Irreducible maps

KW - Locally compact separable metric spaces

UR - http://www.scopus.com/inward/record.url?scp=85132234076&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2022.108161

DO - 10.1016/j.topol.2022.108161

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AN - SCOPUS:85132234076

SN - 0166-8641

VL - 317

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 108161

ER -