|
PlanetMath: classification of topological properties according to behaviour under mapping (407 words) |
 | Topological properties may be classified by their behaviour with respect to mappings. |
| A property of a topological space is called continuous if it is the case that, whenever a space has this property, the images of this space under all continuous mapping also have the same property. |
| This is version 11 of classification of topological properties according to behaviour under mapping, born on 2004-09-24, modified 2006-12-21. |
| topology: Definition and Much More from Answers.com (3576 words) |
| The exact shapes of the pieces constitute a geometric property of the space, and the study of these shapes is in the domain of differential geometry, but the fact that the space has three separate pieces is a qualitative or topological property. |
| There are various properties of a figure, in general, and of a surface such as a sphere, torus, or disk, in particular, that may be used to distinguish between such figures topologically. |
| A traditional joke is that a topologist can't tell the coffee mug she is drinking out of from the doughnut she is eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle. |
Feeds |
Contact