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Map vs Hyperbolic - What's the difference?

map | hyperbolic |

In context|topology|lang=en terms the difference between map and hyperbolic

is that map is (topology)   a continuous function while hyperbolic is (topology) of, pertaining to or in a hyperbolic space (a space having negative curvature or sectional curvature).

As a noun map

is a visual representation of an area, whether real or imaginary.

As a verb map

is to create a visual representation of a territory, etc via cartography.

As a adjective hyperbolic is

of or relating to hyperbole or hyperbolic can be of or pertaining to a hyperbola.

map

English

Noun

(en noun)
  • A visual representation of an area, whether real or imaginary.
  • * {{quote-magazine, year=2012, month=March–April
    • , author= , title=Pixels or Perish , volume=100, issue=2, page=106 , magazine= citation , passage=Drawings and pictures are more than mere ornaments in scientific discourse. Blackboard sketches, geological maps , diagrams of molecular structure, astronomical photographs, MRI images, the many varieties of statistical charts and graphs: These pictorial devices are indispensable tools for presenting evidence, for explaining a theory, for telling a story.}}
  • (mathematics)   A function.
    • The discrete topology is always continuous, therefore functions with discrete domains are always maps.
  • (topology)   A continuous function.
  • A diagram of components of an item.
  • * {{quote-magazine, year=2012, month=March-April
    • , author= , title=Well-connected Brains , volume=100, issue=2, page=171 , magazine=(American Scientist) citation , passage=Creating a complete map of the human connectome would therefore be a monumental milestone but not the end of the journey to understanding how our brains work.}}
  • The butterfly .
  • (UK, old-fashioned)   Someone's face.
  • * {{quote-book
    • , year=1960 , author= , title=(Jeeves in the Offing) , section=chapter X , passage=And as the eye rested on him, he too filled me with pity and terror, for his map was flushed and his manner distraught. He looked like Jack Dempsey at the conclusion of his first conference with Gene Tunney, the occasion, if you remember, when he forgot to duck.}}
  • (board games, computer games)   A predefined and confined imaginary area where a game session takes place.
    • "I don't want to play this map again!"

    Synonyms

    * plan * chart * (mathematics) mapping, function.

    Derived terms

    * argument map * concept map * * mapmaker * mapmaking * mind map * overworld map * texture map * thematic map * topic map

    Related terms

    * atlas * cartographer * cartography

    Verb

    (mapp)
  • To create a visual representation of a territory, etc. via cartography.
  • To inform someone of a particular idea.
  • (mathematics) To act as a function on.
    • f'' maps''' ''A'' to ''B'', ' mapping a\in A to b\in B.
  • (topology) To act as a continuous function on.
    • The discrete topology is always continuous, therefore functions with discrete domains are always mappings.

    Derived terms

    * map out

    Anagrams

    * English three-letter words 1000 English basic words ----

    hyperbolic

    English

    Alternative forms

    * hyperbolick (obsolete)

    Etymology 1

    Adjective

    (en adjective)
  • of or relating to hyperbole
  • using hyperbole: exaggerated
    • This hyperbolical epitaph. — Fuller.
  • * {{quote-news
    • , year=2012 , date=May 20 , author=Nathan Rabin , title=TV: Review: THE SIMPSONS (CLASSIC): “Marge Gets A Job” (season 4, episode 7; originally aired 11/05/1992) , work=The Onion AV Club citation , page= , passage=At the risk of being slightly hyperbolic , the fourth season of The Simpsons is the greatest thing in the history of the universe.}}

    Etymology 2

    Adjective

    (-)
  • Of or pertaining to a hyperbola.
  • * 1988 , R. F. Leftwich, "Wide-Band Radiation Thermometers", chapter 7 of, David P. DeWitt and Gene D. Nutter, editors, Theory and Practice of Radiation Thermometry , ISBN 0471610186, page 512 [http://books.google.com/books?id=SZ6Ldatd7OAC&pg=PA512&dq=hyperbolic]:
    • In this configuration the on-axis image is produced at the real hyperbolic focus (fs2) but off-axis performance suffers.
    • The hyperbolic cosine of zero is one.
  • (mathematics, of a, metric space, or, a geometry) Having negative curvature or sectional curvature.
  • * 1998', Katsuhiko Matsuzaki and Masahiko Taniguchi, '''''Hyperbolic Manifolds and Kleinian Groups , 2002 reprint, , ISBN 0198500629, page 8, proposition 0.10 [http://books.google.com/books?id=DLAGEBfEgEUC&pg=PA8&dq=hyperbolic]:
    • There is a universal constant m_0>0 such that every hyperbolic' surface R has an embedded ' hyperbolic disk with radius greater than m_0.
  • (geometry, topology, of an automorphism) Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.
  • * 2001 , A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups , , ISBN 0521003504, page 6 [http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic]:
    • A hyperbolic isometry f has two (distinct) fixed points on \partial\mathcal H.
  • (topology) Of, pertaining to or in a hyperbolic space (a space having negative curvature or sectional curvature).
  • * 2001 , A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups , , ISBN 0521003504, page 6 [http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic]:
    • Exactly one hypercycle is a hyperbolic geodesic, and this is called the axis A_f of f.
    Derived terms
    * * hyperbolic algebra * hyperbolic angle * hyperbolic automorphism * hyperbolic coordinate * hyperbolic cosecant * hyperbolic cosine * hyperbolic cosine integral * hyperbolic cotangent * hyperbolic cube * hyperbolic cylinder * hyperbolic differential equation * hyperbolic discounting * hyperbolic disk * hyperbolic dodecahedron * hyperbolic fixed point * hyperbolic function * hyperbolic geometry * hyperbolic group * hyperbolic growth * hyperbolic helicoid * hyperbolic icosahedron * hyperbolic inverse function * hyperbolic lemniscate function * hyperbolic link * hyperbolic map * hyperbolic metric * hyperbolic motion * hyperbolic navigation system * hyperbolic octahedron * hyperbolic-orthogonal * hyperbolic orbit * hyperbolic paraboloid * hyperbolic partial differential equation * hyperbolic plane * hyperbolic point * hyperbolic polar sine * hyperbolic polyhedron * hyperbolic polynomial * hyperbolic quaternion * hyperbolic rotation * hyperbolic secant * hyperbolic secant distribution * hyperbolic sector * hyperbolic set * hyperbolic sine * hyperbolic sine integral * hyperbolic small dodecahedral honeycomb * hyperbolic space * hyperbolic tangent * hyperbolic tetrahedron * hyperbolic time chamber * hyperbolic trajectory * hyperbolic triangle * hyperbolic umbilic catastrophe * hyperboloid * quasihyperbolic * subhyperbolic * superhyperbolic