Ask the Chatbot Games & Quizzes History & Society Science & Tech Biographies Animals & Nature Geography & Travel Arts & Culture ProCon Money Videos
abstract space
Directory
References
Discover
Stylish light blue jeans on wooden background, closeup of inset pocket
Why Do Jeans Have That Tiny Pocket?
Nativity Scene, Adoration of the Magi, Church of the Birth of the Virgin Mary, Montenegro
Why Is Christmas in December?
Saint Lucia Day. Young girl wears Lucia crown (tinsel halo) with candles. Holds Saint Lucia Day currant laced saffron buns (lussekatter or Lucia's cats). Observed December 13 honor virgin martyr Santa Lucia (St. Lucy). Luciadagen, Christmas, Sweden
7 Winter Solstice Celebrations From Around the World
Panama Canal infographic
Timeline and Map of the Panama Canal
King Cobra snake in Malaysia. (reptile)
9 of the World’s Deadliest Snakes
Four year old boy with grandfather and father lighting Hanukkah menorah. Photo taken on: December 21st, 2009
Which Is Correct: Hanukkah or Chanukah?
The Battle of Gettysburg, July 1-3, 1863. (Civil War, Pennsylvania)
9 Worst Generals in History

abstract space

mathematics

Learn about this topic in these articles:

Fréchet

topology

  • Because both a doughnut and a coffee cup have one hole (handle), they can be mathematically, or topologically, transformed into one another without cutting them in any way. For this reason, it has often been joked that topologists cannot tell the difference between a coffee cup and a doughnut.
    In topology: Topological equivalence

    …shell, but by adding an abstract fourth dimension it can be removed without any such surgery. Similarly, a closed loop of rope that is tied as a trefoil, or overhand, knot (see figure) in three-dimensional space can be untied in an abstract four-dimensional space.

    Read More