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- Metric_space_aimed_at_its_subspace abstract "In mathematics, a metric space aimed at its subspace is a categorical construction that has a direct geometric meaning. It is also a useful step toward the construction of the metric envelope, or tight span, which are basic (injective) objects of the category of metric spaces.Following (Holsztyński 1966), a notion of a metric space Y aimed at its subspace X is defined.Informally, imagine terrain Y, and its part X, such that wherever in Y you place a sharpshooter, and an apple at another place in Y, and then let the sharpshooter fire, the bullet will go through the apple and will always hit a point of X, or at least it will fly arbitrarily close to points of X – then we say that Y is aimed at X.A priori, it may seem plausible that for a given X the superspaces Y that aim at X can be arbitrarily large or at least huge. We will see that this is not the case. Among the spaces, which aim at a subspace isometric to X there is a unique (up to isometry) universal one, Aim(X), which in a sense of canonical isometric embeddings contains any other space aimed at (an isometric image of) X. And in the special case of an arbitrary compact metric space X every bounded subspace of an arbitrary metric space Y aimed at X is totally bounded (i.e. its metric completion is compact).".
- Metric_space_aimed_at_its_subspace wikiPageID "14114496".
- Metric_space_aimed_at_its_subspace wikiPageLength "4014".
- Metric_space_aimed_at_its_subspace wikiPageOutDegree "12".
- Metric_space_aimed_at_its_subspace wikiPageRevisionID "625754792".
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Category:Metric_geometry.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Category_theory.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Embedding.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Injective_metric_space.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Isometry.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Mathematics.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Metric_map.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Metric_space.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Nachman_Aronszajn.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Tight_span.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Totally_bounded_space.
- Metric_space_aimed_at_its_subspace wikiPageWikiLink Up_to.
- Metric_space_aimed_at_its_subspace wikiPageWikiLinkText "Metric space aimed at its subspace".
- Metric_space_aimed_at_its_subspace wikiPageWikiLinkText "metric space aimed at its subspace".
- Metric_space_aimed_at_its_subspace wikiPageUsesTemplate Template:Citation.
- Metric_space_aimed_at_its_subspace wikiPageUsesTemplate Template:Harv.
- Metric_space_aimed_at_its_subspace subject Category:Metric_geometry.
- Metric_space_aimed_at_its_subspace hypernym Construction.
- Metric_space_aimed_at_its_subspace type Company.
- Metric_space_aimed_at_its_subspace comment "In mathematics, a metric space aimed at its subspace is a categorical construction that has a direct geometric meaning.".
- Metric_space_aimed_at_its_subspace label "Metric space aimed at its subspace".
- Metric_space_aimed_at_its_subspace sameAs Q6824328.
- Metric_space_aimed_at_its_subspace sameAs m.03cv1s0.
- Metric_space_aimed_at_its_subspace sameAs Q6824328.
- Metric_space_aimed_at_its_subspace wasDerivedFrom Metric_space_aimed_at_its_subspace?oldid=625754792.
- Metric_space_aimed_at_its_subspace isPrimaryTopicOf Metric_space_aimed_at_its_subspace.