I'm reading Topology by Munkres, and I'm having some trouble with exercise 5 on page 92 (screenshot attached).
Homework Statement
Let X and X' denote a single set in the topologies T and T', respectively; let Y and Y' denote a single set in the topologies U and U', respectively. Assume...
Ok, here are all the definitions that have been used:
The power set P(X) of a set X is a lattice, with A \preceq B defined as A \subset B. Now a subset U of P(X) is an upper set if \forall a,b \in P(x) with a \subset b, a \in U implies b \in U .
A filter F on X is a family of subsets of...
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The textbook I'm using states Kepler's first law in the following form: all planets move in elliptical paths with the sun at one of the foci. If I'm understanding this claim correctly, I've got some problems with it..
This conclusion was reached using a potential that depends only on the...