Preservation of Topological Properties
- every disjoint union of discrete spaces is discrete
- Separation
- every disjoint union of T0 spaces is T0
- every disjoint union of T1 spaces is T1
- every disjoint union of Hausdorff spaces is Hausdorff
- Connectedness
- the disjoint union of two or more nonempty topological spaces is disconnected
Read more about this topic: Disjoint Union (topology)
Famous quotes containing the words preservation of, preservation and/or properties:
“It is my hope to be able to prove that television is the greatest step forward we have yet made in the preservation of humanity. It will make of this Earth the paradise we have all envisioned, but have never seen.”
—Joseph O’Donnell. Clifford Sanforth. Professor James Houghland, Murder by Television, just before he demonstrates his new television device (1935)
“I do seriously believe that if we can measure among the States the benefits resulting from the preservation of the Union, the rebellious States have the larger share. It destroyed an institution that was their destruction. It opened the way for a commercial life that, if they will only embrace it and face the light, means to them a development that shall rival the best attainments of the greatest of our States.”
—Benjamin Harrison (1833–1901)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)