Definition of "homeomorphism" []

• Chemistry A close similarity in the crystal forms of unlike compounds. (noun)
• Mathematics A continuous bijection between two figures whose inverse is also continuous. (noun)

American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

• "A homeomorphism is, essentially, a one-to-one correspondence (see any maths site for details)."
• "One is that it is a homeomorphism invariant: if two spaces are homeomorphic, then they have the same fundamental group."
• "The topology on the countable product of the two-point space '' D '' is induced by the metric The Cantor set may be embedded in the unit interval by the map which is a homeomorphism onto the subset of the unit interval obtained by iteratively deleting the middle third of each interval compact."