@MISC{UNIFORM1.MIZ,
  AUTHOR = {Nakamura, Yatsuka and Trybulec, Andrzej},
  TITLE = {{L}ebesgue's Covering Lemma, Uniform Continuity
and Segmentation of Arcs},
  SECTION1 = {Lebesgue's Covering Lemma},
  SECTION2 = {Uniformity of Continuous Functions on Compact Spaces},
  SECTION3 = {Segmentation of Arcs},
  DAY = {13},
  MONTH = {November},
  YEAR = {1997},
  ADDRESS1 = {Shinshu University\\Nagano},
  ADDRESS2 = {University of Bia{\l}ystok},
  SUMMARY = {For mappings from a metric space to a metric space, a notion of
uniform continuity is defined. If we introduce natural topologies
to the metric spaces, a uniformly continuous function becomes continuous.
    On the other hand, if the domain is compact, a continuous function
is uniformly continuous. For this proof, Lebesgue's covering lemma is
also proved.
    An arc, which is homeomorphic to [0,1], can be divided into small
segments, as small as one wishes.}}

