×

zbMATH — the first resource for mathematics

An embedding theorem for certain spaces with an equidistant property. (English) Zbl 0336.54032

MSC:
54E99 Topological spaces with richer structures
54C25 Embedding
54F99 Special properties of topological spaces
54F65 Topological characterizations of particular spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anthony D. Berard Jr., Characterizations of metric spaces by the use of their midsets: Intervals, Fund. Math. 73 (1971/72), no. 1, 1 – 7. · Zbl 0223.54017
[2] A. D. Berard Jr. and W. Nitka, A new definition of the circle by the use of bisectors, Fund. Math. 85 (1974), no. 1, 49 – 55. · Zbl 0281.53042
[3] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. · Zbl 0060.39808
[4] K. Kuratowski, S. B. Nadler Jr., and G. S. Young, Continuous selections on locally compact separable metric spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 5 – 11 (English, with Loose Russian summary). · Zbl 0191.53404
[5] A. Lelek and W. Nitka, On convex metric spaces. I, Fund. Math. 49 (1960/1961), 183 – 204. · Zbl 0171.21601
[6] L. D. Loveland and J. E. Valentine, Characterizing a circle with the double midset property, Proc. Amer. Math. Soc. 53 (1975), no. 2, 443 – 444. · Zbl 0317.52003
[7] L. D. Loveland and J. E. Valentine, Convex metric spaces with 0-dimensional midsets, Proc. Amer. Math. Soc. 37 (1973), 568 – 571. · Zbl 0252.52009
[8] -, Generalized midset properties characterize geodesic circles and intervals (preprint). · Zbl 0382.52003
[9] L. D. Loveland and S. G. Wayment, Characterizing a curve with the double midset property, Amer. Math. Monthly 81 (1974), 1003 – 1006. · Zbl 0291.54042 · doi:10.2307/2319308 · doi.org
[10] Edwin W. Miller, On Subsets of a Continuous Curve which Lie on an Arc of the Continuous Curve, Amer. J. Math. 54 (1932), no. 2, 397 – 416. · Zbl 0004.27402 · doi:10.2307/2371004 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.