Topology
From Vectorcalcumb
(Difference between revisions)
| Line 9: | Line 9: | ||
<li>Exterior point of a set. Exterior of a set.</li> | <li>Exterior point of a set. Exterior of a set.</li> | ||
<li>Boundary point of a set. Boundary of a set.</li> | <li>Boundary point of a set. Boundary of a set.</li> | ||
| - | <li>Compact sets. | + | <li>Compact sets.</li> |
| + | <li>Acumulation point of a set.</li> | ||
</ul><li> | </ul><li> | ||
<li>The "ball" topology on R<sup>n</sup></li> | <li>The "ball" topology on R<sup>n</sup></li> | ||
| Line 23: | Line 24: | ||
<li>Open sets in the norm-infinity topology.</li> | <li>Open sets in the norm-infinity topology.</li> | ||
</ul> | </ul> | ||
| + | <li>Fact: The "ball" topology on R<sup>n</sup> is the same as the "box" topology on R<sup>n</sup></li> | ||
| + | <li>Induced topology on a subset of R<sup>n</sup></li> | ||
</ul> | </ul> | ||
Revision as of 01:15, 7 February 2006
Topology
- What is a topology on a set?
- Open sets.
- Closed sets.
- Neighborhood of a point.
- Interior points of a set. Interior of a set.
- Exterior point of a set. Exterior of a set.
- Boundary point of a set. Boundary of a set.
- Compact sets.
- Acumulation point of a set.
- The "ball" topology on Rn
- The norm-2 on Rn.
- Open balls in norm-2.
- Open sets in the norm-2 topology.
- The "box" topology on Rn
- The norm-infinity on Rn.
- Open balls in norm-infinity.
- Open sets in the norm-infinity topology.
- Fact: The "ball" topology on Rn is the same as the "box" topology on Rn
- Induced topology on a subset of Rn
