The Alexandroff one-point compactification as a prototype for extensions
نویسندگان
چکیده
منابع مشابه
Metrization of the One-point Compactification
A new, more widely applicable, constructive definition of locally compact metric space is given, and a metric one-point compactification is constructed. Classically, this provides a simpler, more direct, construction of a metric on the one-point compactification of a separable locally compact metric
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A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...
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x->y,x=y,y->x holds. Here x -+ y expresses the fact that {x, y} e -+ and we sometimes write this in the alternative form y <--x . Extending the notation to subsets of T we write A --+ B or B is a subtournament of .l, and i is an extension of ,T', if T' e T and -+' is the restriction of --+ to T' ; we will usually writ...
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A one-point extension of an egglike inversive plane of order n exists if, and only if, n is 2 or 3. Hence there are no 4-(18,6,1) designs and no 4-(66,10,1) designs. An inversive plane of order n is a one-point extension of an affine plane of ordern, that is, a 3-(n + 1,n + 1,1) design. An ovoid of PG(3, q), q > 2, is a set of q2 + 1 points, no three collinear. An ovoid of PG(3, 2) is a set of ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2012
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.07.008