Homogeneity and isotropy of matter at the largest scales would suggest that the largest discrete structures are parts of a single indiscrete form, like the crumbs which make up the interior of a cake.
22.
In the two extremes, every set can be open ( called the discrete topology ), or no set can be open but the space itself and the empty set ( the indiscrete topology ).
23.
:Note that the indiscrete space is indeed a ( 0-dimensional ) manifold if the space in question has precisely one-point or vacuously a manifold if the space in question is empty.
24.
Little by little he gained imitators and, always ready to reply to questions of taste and even enquiries from the indiscrete curious, Du Sommerard welcomed people to see his collection and gave lessons in practical archaeology.
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Sen . John McCain's father blended heroics in uniform with a tendency to swear, drink too much, and make indiscrete comments, according to excerpts of a new book by McCain about his family history.
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The indiscrete topology is also known as the "'biggest "'or "'chaotic "'topology, and it is generated by the pretopology which has only isomorphisms for covering families.
27.
Where the discrete topology is initial or free, the indiscrete topology is final or cofree : every function " from " a topological space " to " an indiscrete space is continuous, etc.
28.
Where the discrete topology is initial or free, the indiscrete topology is final or cofree : every function " from " a topological space " to " an indiscrete space is continuous, etc.
29.
We cannot eliminate the Hausdorff condition; a countable set with the indiscrete topology is compact, has more than one point, and satisfies the property that no one point sets are open, but is not uncountable.
30.
:: : Gian-Carlo Rota answered this question in his " Indiscrete Thoughts ", speaking of Alonzo Church, see Fine Hall in its golden age : Remembrances of Princeton in the early fifties.
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