scholarly journals On product of spaces of quasicomponents

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6307-6311
Author(s):  
Gjorgji Markoski ◽  
Abdulla Buklla
Keyword(s):  
Product Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Topological Properties ◽  
Locally Compact

We use a characterization of quasicomponents by continuous functions to obtain the well known theorem which states that product of quasicomponents Qx,Qy of topological spaces X,Y, respectively, gives quasicomponent in the product space X x Y. If spaces X,Y are locally-compact, paracompact and Haussdorf, then we prove that the space of quasicomponents of the product Q(XxY) is homeomorphic with the product space Q(X) x Q(Y), so these two spaces have the same topological properties.

scholarly journals Orderability of topological spaces by continuous preferences

2001 ◽  
Vol 27 (8) ◽  
pp. 505-512 ◽  
Author(s):  
José Carlos Rodríguez Alcantud
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Properties ◽  
Linear Orders ◽  
Mathematical Economics

We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf. Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a topological space is obtained.

scholarly journals Continuity of Convolution of Test Functions on Lie Groups

2014 ◽  
Vol 66 (1) ◽  
pp. 102-140
Author(s):  
Lidia Birth ◽  
Helge Glöckner
Keyword(s):  
Continuous Functions ◽  
Locally Convex Space ◽  
Locally Compact Group ◽  
Locally Convex Spaces ◽  
Test Functions ◽  
Bilinear Map ◽  
Locally Compact ◽  
Compactly Supported ◽  
Locally Convex

AbstractFor a Lie group G, we show that the map taking a pair of test functions to their convolution, is continuous if and only if G is σ-compact. More generally, consider with t ≤ r + s, locally convex spaces E1, E2 and a continuous bilinear map b : E1 × E2 → F to a complete locally convex space F. Let be the associated convolution map. The main result is a characterization of those (G; r; s; t; b) for which β is continuous. Convolution of compactly supported continuous functions on a locally compact group is also discussed as well as convolution of compactly supported L1-functions and convolution of compactly supported Radon measures.

Natural extension of EF-spaces and EZ-spaces to the pointfree context

2019 ◽  
Vol 69 (5) ◽  
pp. 979-988
Author(s):  
Jissy Nsonde Nsayi
Keyword(s):  
Closed Subset ◽  
Natural Extension ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Tychonoff Space ◽  
Regular Closed

Abstract Two problems concerning EF-frames and EZ-frames are investigated. In [Some new classes of topological spaces and annihilator ideals, Topology Appl. 165 (2014), 84–97], Tahirefar defines a Tychonoff space X to be an EF (resp., EZ)-space if disjoint unions of clopen sets are completely separated (resp., every regular closed subset is the closure of a union of clopen subsets). By extending these notions to locales, we give several characterizations of EF and EZ-frames, mostly in terms of certain ring-theoretic properties of 𝓡 L, the ring of real-valued continuous functions on L. We end by defining a qsz-frame which is a pointfree context of qsz-space and, give a characterization of these frames in terms of rings of real-valued continuous functions on L.

TWO SPACES OF MINIMAL PRIMES

2012 ◽  
Vol 11 (01) ◽  
pp. 1250014 ◽  
Author(s):  
PAPIYA BHATTACHARJEE
Keyword(s):  
Compact Space ◽  
Hausdorff Space ◽  
Topological Spaces ◽  
Zariski Topology ◽  
Topological Properties ◽  
Locally Compact ◽  
Inverse Topology ◽  
Minimal Prime ◽  
Stone Spaces ◽  
Prime Elements

This paper studies algebraic frames L and the set Min (L) of minimal prime elements of L. We will endow the set Min (L) with two well-known topologies, known as the Hull-kernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min (L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min (L) endowed with the inverse topology is a T1, compact space. The main goal will be to find conditions on L for the spaces Min (L) and Min (L)-1 to have various topological properties; for example, compact, locally compact, Hausdorff, zero-dimensional, and extremally disconnected. We will also discuss when the two topological spaces are Boolean and Stone spaces.

scholarly journals Isomorphisms from Extremely Regular Subspaces of C0K into C0S,X Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Manuel Felipe Cerpa-Torres ◽  
Michael A. Rincón-Villamizar
Keyword(s):  
Banach Space ◽  
Compact Hausdorff Space ◽  
Geometrical Parameter ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Continuous Image ◽  
Topological Properties ◽  
Locally Compact ◽  
Regular Subspace ◽  
Locally Compact Hausdorff Space

For a locally compact Hausdorff space K and a Banach space X, let C0K,X be the Banach space of all X-valued continuous functions defined on K, which vanish at infinite provided with the sup norm. If X is ℝ, we denote C0K,X as C0K. If AK be an extremely regular subspace of C0K and T:AK⟶C0S,X is an into isomorphism, what can be said about the set-theoretical or topological properties of K and S? Answering the question, we will prove that if X contains no copy of c0, then the cardinality of K is less than that of S. Moreover, if TT−1<3 and AK is also a subalgebra of C0K, the cardinality of the αth derivative of K is less than that of the αth derivative of S, for each ordinal α. Finally, if λX>1 and TT−1<λX, then K is a continuous image of a subspace of S. Here, λX is the geometrical parameter introduced by Jarosz in 1989: λX=infmaxx+λy:λ=1:x=y=1. As a consequence, we improve classical results about into isomorphisms from extremely regular subspaces already obtained by Cengiz.

scholarly journals On the Fuzzy Number Space with the Level Convergence Topology

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. J. Font ◽  
A. Miralles ◽  
M. Sanchis
Keyword(s):  
Topological Space ◽  
Fuzzy Number ◽  
Continuous Functions ◽  
Topological Properties ◽  
Compact Sets ◽  
Compact Open Topology ◽  
Locally Compact ◽  
Compact Topological Space ◽  
Convergence Topology

We characterize compact sets of𝔼1endowed with the level convergence topologyτℓ. We also describe the completion(𝔼1̂,𝒰̂)of𝔼1with respect to its natural uniformity, that is, the pointwise uniformity𝒰, and show other topological properties of𝔼1̂, as separability. We apply these results to give an Arzela-Ascoli theorem for the space of(𝔼1,τℓ)-valued continuous functions on a locally compact topological space equipped with the compact-open topology.

scholarly journals Multipliers from spaces of test functions to amalgams

1993 ◽  
Vol 54 (1) ◽  
pp. 97-110
Author(s):  
Maria Torres De Squire
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Compact Abelian Group ◽  
Continuous Functions ◽  
Locally Compact Abelian Group ◽  
Test Functions ◽  
Space Of Continuous Functions ◽  
Locally Compact ◽  
The Fourier Transform

AbstractIn this paper we study the space of multipliers M(r, s: p, q) from the space of test functions Φrs(G), on a locally compact abelian group G, to amalgams (Lp, lq)(G); the former includes (when r = s = ∞) the space of continuous functions with compact support and the latter are extensions of the Lp(G) spaces. We prove that the space M(∞: p) is equal to the derived space (Lp)0 defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.

A Class of Function Algebras

1960 ◽  
Vol 12 ◽  
pp. 353-362 ◽  
Author(s):  
F. W. Anderson
Keyword(s):  
Continuous Functions ◽  
Regular Space ◽  
Locally Compact ◽  
Completely Regular ◽  
Compact Spaces ◽  
The Past ◽  
Function Algebras ◽  
Bounded Continuous Functions ◽  
Locally Compact Spaces

A problem which has generated considerable interest during the past couple of decades is that of characterizing abstractly systems of realvalued continuous functions with various algebraic or topological-algebraic structures. With few exceptions known characterizations are of systems of bounded continuous functions on compact or locally compact spaces. Only recently have characterizations been given of the systems C(X) of all realvalued continuous functions on an arbitrary completely regular space X (1). One of the main objects of this paper is to provide, by using certain special techniques, a characterization of C(X) for a particular class of (not necessarily compact) completely regular spaces.

Every Hausdorff Compactification of a Locally Compact Separable Space is a Ga Compactification

1977 ◽  
Vol 29 (1) ◽  
pp. 125-131
Author(s):  
J. Van Mill
Keyword(s):  
Topological Spaces ◽  
Separable Space ◽  
Locally Compact ◽  
Complete Regularity ◽  
Intrinsic Characterization ◽  
Hausdorff Compactifications

In [4], De Groot and Aarts constructed Hausdorff compactifications of topological spaces to obtain a new intrinsic characterization of complete regularity. These compactifications were called GA compactifications in [5] and [7]. A characterization of complete regularity was earlier given by Frink [3], by means of Wallman compactifications, a method which led to the intriguing problem of whether every Hausdorff compactification is a Wallman compactification.

Voiculescu amenable Hopf von Neumann algebras with applications

2016 ◽  
Vol 15 (06) ◽  
pp. 1650079 ◽  
Author(s):  
Fatemeh Akhtari ◽  
Rasoul Nasr-Isfahani
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Continuous Functions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann

For a Hopf von Neumann algebra [Formula: see text], we give a fixed point characterization of Voiculescu amenability of [Formula: see text] in terms of modules over [Formula: see text]. As a consequence, we present some descriptions for amenability of locally compact groups in terms of certain associated Hopf von Neumann algebras. We finally apply this result to some modules of continuous functions on a multiplicative subsemigroup of [Formula: see text].

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