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In mathematics, the notion of externology in a topological space X generalizes the basic properties of the family
εXcc = {E ⊆ X : X\E is a closed compact subset of X}
of complements of the closed compact subspaces of X, which are used to construct its Alexandroff compactification. An externology permits to introduce a notion of end[1] point, to study the divergence of nets in terms of convergence to end points and it is a useful tool for the study and classification of some families of non compact topological spaces. It can also be used to approach a topological space as the limit of other topological spaces: the externologies are very useful when a compact metric space embedded in a Hilbert space is approached by its open neighbourhoods.
An exteriorspace (X,τ,ε) consists of a topological space (X,τ) together with an externology ε. An open E which is in ε is said to be an exterior-open...
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was...
elements of an exterior power of the cotangent space at p. When the exterior algebra is viewed as a quotient of the tensor algebra, the exterior product corresponds...
in general topology Exteriorspace Hausdorff space – Type of topological space Hilbert space – Type of topological vector space Hemicontinuity Linear...
describe the expansion; the way we define space in our universe in no way requires additional exteriorspace into which it can expand, since an expansion...
nature, all have a similar conical exterior façade that is a landmark for the respective park. The original Space Mountain coaster opened in 1975 at Walt...
expected to use this boundary to partition 2-dimensional space into an interior and exterior. Surface (3-dimensional), represented using a variety of...
or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear...
horizontal subspace. If ϕ is a k-form on P with values in a vector space V, then its exterior covariant derivative Dϕ is a form defined by D ϕ ( v 0 , v 1 ...
relationship between exhibition space and the surrounding space, and the exterior. It is characteristic for the spaces in Blaisse's work to merge via a...
Hardy space to be completely characterized by the spaces of inner and outer functions. One says that G(z)[clarification needed] is an outer (exterior) function...
mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an...
that the users of the building move freely from the interior space to the exteriorspace. The rectangle on the northeast portion of the site, called "the...
of dwelling interiors with exteriorspaces and the placement of windows to allow residents to naturally survey the exterior and interior public areas of...
atlas, as the patches naturally provide charts, and since there is no exteriorspace involved it leads to an intrinsic view of the manifold. The manifold...
various spin-offs. While a TARDIS is capable of disguising itself, the exterior appearance of the Doctor's TARDIS typically mimics a police box, an obsolete...
Bernal sphere Exterior of a Bernal sphere A Bernal sphere next to a solar power satellite and an asteroid mining station Dyson sphere Space habitat O'Neill...
inspect the exterior of the shuttle for damage to the thermal protection system. In 1969, Canada was invited by the National Aeronautics and Space Administration...
{v} _{1}} yields the exterior algebra. A vector bundle is a family of vector spaces parametrized continuously by a topological space X. More precisely,...
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