A quest for nice kernels of neighbourhood assignments
نویسنده
چکیده
Given a topological property (or a class) P, the class P∗ dual to P (with respect to neighbourhood assignments) consists of spaces X such that for any neighbourhood assignment {Ox : x ∈ X} there is Y ⊂ X with Y ∈ P and S {Ox : x ∈ Y } = X. The spaces from P∗ are called dually P. We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define D-spaces. We prove a number of results on duals of some general classes of spaces establishing, in particular, that any generalized ordered space of countable extent is dually discrete.
منابع مشابه
Classes defined by stars and neighbourhood assignments ✩
We apply and develop an idea of E. van Douwen used to define D-spaces. Given a topological property P , the class P∗ dual to P (with respect to neighbourhood assignments) consists of spaces X such that for any neighbourhood assignment {Ox : x ∈X} there is Y ⊂X with Y ∈P and {Ox : x ∈ Y } =X. We prove that the classes of compact, countably compact and pseudocompact are self-dual with respect to ...
متن کاملThe Neighbourhood Polynomial of some Nanostructures
The neighbourhood polynomial G , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. In other word $N(G,x)=sum_{Uin N(G)} x^{|U|}$, where N(G) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. In this paper we compute this polynomial for some na...
متن کاملQuest-V: A Virtualized Multikernel for High-Confidence Systems
This paper outlines the design of ‘Quest-V’, which is implemented as a collection of separate kernels operating together as a distributed system on a chip. Quest-V uses virtualization techniques to isolate kernels and prevent local faults from affecting remote kernels. This leads to a high-confidence multikernel approach, where failures of system subcomponents do not render the entire system in...
متن کاملConditionally Positive Definite Kernels and Pontryagin Spaces
Conditionally positive definite kernels provide a powerful tool for scattered data approximation. Many nice properties of such methods follow from an underlying reproducing kernel structure. While the connection between positive definite kernels and reproducing kernel Hilbert spaces is well understood, the analog relation between conditionally positive definite kernels and reproducing kernel Po...
متن کاملPredictable migration and communication in the Quest-V multikernal
Quest-V is a system we have been developing from the ground up, with objectives focusing on safety, predictability and efficiency. It is designed to work on emerging multicore processors with hardware virtualization support. Quest-V is implemented as a “distributed system on a chip” and comprises multiple sandbox kernels. Sandbox kernels are isolated from one another in separate regions of phys...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010