Peano compactifications and property  metric spaces

Dickman, R. F.

Peano compactifications and property metric spaces

dc.contributor.author	Dickman, R. F.	en
dc.contributor.department	Mathematics	en
dc.date.accessioned	2017-09-18T10:13:01Z	en
dc.date.available	2017-09-18T10:13:01Z	en
dc.date.issued	1980-01-01	en
dc.date.updated	2017-09-18T10:13:01Z	en
dc.description.abstract	Let (X,d) denote a locally connected, connected separable metric space. We say the X is S-metrizable provided there is a topologically equivalent metric ρ on X such that (X,ρ) has Property S, i.e. for any ϵ>0, X is the union of finitely many connected sets of ρ-diameter less than ϵ. It is well-known that S-metrizable spaces are locally connected and that if ρ is a Property S metric for X, then the usual metric completion (X˜,ρ˜) of (X,ρ) is a compact, locally connected, connected metric space, i.e. (X˜,ρ˜) is a Peano compactification of (X,ρ). There are easily constructed examples of locally connected connected metric spaces which fail to be S-metrizable, however the author does not know of a non-S-metrizable space (X,d) which has a Peano compactification. In this paper we conjecture that: If (P,ρ) a Peano compactification of (X,ρ\|X), X must be S-metrizable. Several (new) necessary and sufficient for a space to be S-metrizable are given, together with an example of non-S-metrizable space which fails to have a Peano compactification.	en
dc.description.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	R. F. Dickman Jr., “Peano compactifications and property metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 3, no. 4, pp. 695-700, 1980. doi:10.1155/S016117128000049X	en
dc.identifier.doi	https://doi.org/10.1155/S016117128000049X	en
dc.identifier.uri	http://hdl.handle.net/10919/79128	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Peano compactifications and property metric spaces	en
dc.title.serial	International Journal of Mathematics and Mathematical Sciences	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en