Search results for "Topological space"
showing 10 items of 54 documents
Matemātika
2005
New applications of extremely regular function spaces
2017
Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.
On two topological cardinal invariants of an order-theoretic flavour
2012
Noetherian type and Noetherian $\pi$-type are two cardinal functions which were introduced by Peregudov in 1997, capturing some properties studied earlier by the Russian School. Their behavior has been shown to be akin to that of the \emph{cellularity}, that is the supremum of the sizes of pairwise disjoint non-empty open sets in a topological space. Building on that analogy, we study the Noetherian $\pi$-type of $\kappa$-Suslin Lines, and we are able to determine it for every $\kappa$ up to the first singular cardinal. We then prove a consequence of Chang's Conjecture for $\aleph_\omega$ regarding the Noetherian type of countably supported box products which generalizes a result of Lajos S…
Topological Space
2020
We introduce some formal definition of Topological Space in the the framework of the so-called classical mathematics.
σ-Continuous and Co-σ-continuous Maps
2009
In this chapter we isolate the topological setting that is suitable for our study. We first present 2.1–2.3 to follow an understandable logical scheme nevertheless the main contribution are presented in 2.4–2.7 and our main tool will be Theorem 2.32. An important concept will be the σ-continuity of a map Φ from a topological space (X, T) into a metric space (Y, g). The σ-continuity property is an extension of continuity suitable to deal with countable decompositions of the domain space X as well as with pointwise cluster points of sequences of functions Φn : X → Y, n = 1,2,… When (X,T) is a subset of a locally convex linear topological space we shall refine our study to deal with σ-slicely …
Between striated and smooth space: Exploring the topology of transnational student mobility
2017
In this paper, we raise a question regarding how transnational students develop their spaces as mobile, temporary, and at times stable and territorially fixed. We argue that approaching transnational student migration and its relations to place as a Deleuzian assemblage is a fruitful way of highlighting this issue, and we propose the axes of the expressive/material and territorialisation/de-territorialisation as analytical tools for understanding aspects of the temporal and spatial dimensions of transnational student mobility. Our theoretical discussion is informed by the migration experiences of transnational students studying at a Norwegian university. Our core argument is that transnatio…
A fuzzification of the category of M-valued L-topological spaces
2004
[EN] A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.
Sobriety and spatiality in varieties of algebras
2008
The paper considers a generalization of the classical Papert-Papert-Isbell adjunction between the categories of topological spaces and locales to an arbitrary variety of algebras and illustrates the obtained results by the category of algebras over a given unital commutative quantale.
Hasse diagrams and orbit class spaces
2011
Abstract Let X be a topological space and G be a group of homeomorphisms of X. Let G ˜ be an equivalence relation on X defined by x G ˜ y if the closure of the G-orbit of x is equal to the closure of the G-orbit of y. The quotient space X / G ˜ is called the orbit class space and is endowed with the natural order inherited from the inclusion order of the closure of the classes, so that, if such a space is finite, one can associate with it a Hasse diagram. We show that the converse is also true: any finite Hasse diagram can be realized as the Hasse diagram of an orbit class space built from a dynamical system ( X , G ) where X is a compact space and G is a finitely generated group of homeomo…
Compactifying Torus Fibrations Over Integral Affine Manifolds with Singularities
2021
This is an announcement of the following construction: given an integral affine manifold B with singularities, we build a topological space X which is a torus fibration over B. The main new feature of the fibration X → B is that it has the discriminant in codimension 2.