Geodesic
A Note on Extending Locally Finite Collections
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 117-119

Voir la notice de l'article provenant de la source Cambridge University Press

Recently there has been a great deal of interest in extending refinements of locally finite and point finite collections on subsets of certain topological spaces. In particular the first named author showed that a subset S of a topological space X is P-embedded in X if and only if every locally finite cozero-set cover on S has a refinement that can be extended to a locally finite cozero-set cover of X. Since then many authors have studied similar types of embeddings (see [1], [2], [3], [4], [6], [8], [9], [10], [11], and [12]). Since the above characterization of P-embedding is equivalent to extending continuous pseudometrics from the subspace S up to the whole space X, it is natural to wonder when can a locally finite or a point finite open or cozero-set cover on S be extended to a locally finite or point-finite open or cozero-set cover on X. 
A Note on Extending Locally Finite Collections. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 117-119. doi: 10.4153/CMB-1976-018-9
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