Topology
From Vectorcalcumb
(Difference between revisions)
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<ul> | <ul> | ||
<li>Open sets.</li> | <li>Open sets.</li> | ||
+ | <p>Sets which do not contain their boundary</p> | ||
<li>Closed sets.</li> | <li>Closed sets.</li> | ||
<li>Neighborhood of a point.</li> | <li>Neighborhood of a point.</li> |
Revision as of 04:47, 8 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.
Sets which do not contain their boundary
- 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