TY - JOUR
T1 - On fiber diameters of continuous maps
AU - Landweber, Peter S.
AU - Lazar, Emanuel A.
AU - Patel, Neel
N1 - Publisher Copyright:
© THE MATHEMATICAL ASSOCIATION OF AMERICA.
PY - 2016
Y1 - 2016
N2 - We present a surprisingly short proof that for any continuous map f: ℝn → ℝm, if n > m, then there exists no bound on the diameter of fibers of f. Moreover, we show that when m = 1, the union of small fibers of f is bounded; when m > 1, the union of small fibers need not be bounded. Applications to data analysis are considered.
AB - We present a surprisingly short proof that for any continuous map f: ℝn → ℝm, if n > m, then there exists no bound on the diameter of fibers of f. Moreover, we show that when m = 1, the union of small fibers of f is bounded; when m > 1, the union of small fibers need not be bounded. Applications to data analysis are considered.
UR - http://www.scopus.com/inward/record.url?scp=84975514953&partnerID=8YFLogxK
U2 - 10.4169/amer.math.monthly.123.4.392
DO - 10.4169/amer.math.monthly.123.4.392
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84975514953
SN - 0002-9890
VL - 123
SP - 392
EP - 397
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 4
ER -