General position properties satisfied by finite products of dendrites

Author:
Philip L. Bowers

Journal:
Trans. Amer. Math. Soc. **288** (1985), 739-753

MSC:
Primary 54F50; Secondary 54C25, 54C35, 54F35

DOI:
https://doi.org/10.1090/S0002-9947-1985-0776401-5

MathSciNet review:
776401

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Abstract: Let be a dendrite whose endpoints are dense and let be the complement in of a dense -compact collection of endpoints of . This paper investigates various general position properties that finite products of and possess. In particular, it is shown that (i) if is an -space that satisfies the disjoint -cells property, then satisfies the disjoint -cells property, (ii) is a compact -dimensional that satisfies the disjoint -cells property, (iii) is a compact -dimensional that satisfies the stronger general position property that maps of -dimensional compacta into are approximable by both -maps and -embeddings, and (iv) is a topologically complete -dimensional that satisfies the discrete -cells property and as such, maps from topologically complete separable -dimensional spaces into are strongly approximable by closed -embeddings.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0776401-5

Keywords:
Disjoint -cells property,
discrete -cells property,
locally -connected in

Article copyright:
© Copyright 1985
American Mathematical Society