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computably based locally compact をテンプレートにして作成
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*Definition [#y7e8ff71]
-A computably based locally compact space consists of a set of codes
for basic “points”, “open” and “compact” subspaces, together with an interpretation of
these codes in a locally compact [[sober space]]. We require of the space that every open
subspace be a union of basic ones. We also want to be able to compute
++ codes (that we shall just call 0 and 1) for the empty set and the entire space, considered
as open and compact subspaces (if, that is, the entire space is in fact compact);
++ codes for the union and intersection of two open subspaces, and for the union of two
compact ones, given their codes (we write + and ⋆ instead of ∪ and ∩ for these binary
operations, to emphasise that they act on codes, rather than on the subspaces that the
codes name);
++ whether a particular representable point belongs to a particular basic open subspace,
given their codes; but we only need a positive answer to this question if there is one, as
failure of the property is indicated by non-termination;
++ more generally, whether an open subspace includes a compact one, given their codes;
++ codes for U and K such that L ⊂ U ⊂ K ⊂ V , given codes for L ⊂ V as above.
++ In fact, we shall require the basic compact and open subspaces to come in pairs, with
U_n ⊂ K_n as in [JS96], where the superscript n names the pair, and we also need part
v. to yield such a pair as the interpolant.
*Reference [#m582883e]
-Taylor, Paul , ''Computably based locally compact spaces.''[J] Log. Methods Comput. Sci. 2, No. 1, Paper 1, 70 p., electronic only (2006).
-[JS96] Jung, Achim and Sünderhauf, Philipp ''On the duality of compact vs. open.''[A] Andima, Susan (ed.) et al., Papers on general topology and applications. Papers presented at the 11th summer conference at the University of Southern Mai
終了行:
*Definition [#y7e8ff71]
-A computably based locally compact space consists of a set of codes
for basic “points”, “open” and “compact” subspaces, together with an interpretation of
these codes in a locally compact [[sober space]]. We require of the space that every open
subspace be a union of basic ones. We also want to be able to compute
++ codes (that we shall just call 0 and 1) for the empty set and the entire space, considered
as open and compact subspaces (if, that is, the entire space is in fact compact);
++ codes for the union and intersection of two open subspaces, and for the union of two
compact ones, given their codes (we write + and ⋆ instead of ∪ and ∩ for these binary
operations, to emphasise that they act on codes, rather than on the subspaces that the
codes name);
++ whether a particular representable point belongs to a particular basic open subspace,
given their codes; but we only need a positive answer to this question if there is one, as
failure of the property is indicated by non-termination;
++ more generally, whether an open subspace includes a compact one, given their codes;
++ codes for U and K such that L ⊂ U ⊂ K ⊂ V , given codes for L ⊂ V as above.
++ In fact, we shall require the basic compact and open subspaces to come in pairs, with
U_n ⊂ K_n as in [JS96], where the superscript n names the pair, and we also need part
v. to yield such a pair as the interpolant.
*Reference [#m582883e]
-Taylor, Paul , ''Computably based locally compact spaces.''[J] Log. Methods Comput. Sci. 2, No. 1, Paper 1, 70 p., electronic only (2006).
-[JS96] Jung, Achim and Sünderhauf, Philipp ''On the duality of compact vs. open.''[A] Andima, Susan (ed.) et al., Papers on general topology and applications. Papers presented at the 11th summer conference at the University of Southern Mai
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