Topological properties of locally compact connected Minkowski planes and their derived affine planes

1989 ◽  
Vol 32 (3) ◽  
Author(s):  
G�nterF. Steinke
Keyword(s):  
Topological Properties ◽  
Locally Compact ◽  
Affine Planes ◽  
Minkowski Planes

scholarly journals Onθ-regular spaces

1994 ◽  
Vol 17 (4) ◽  
pp. 687-692 ◽  
Author(s):  
Martin M. Kovár
Keyword(s):  
Regular Space ◽  
Topological Properties ◽  
Locally Compact ◽  
Basic Properties ◽  
Paracompact Space ◽  
Paracompact Spaces

In this paper we studyθ-regularity and its relations to other topological properties. We show that the concepts ofθ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces areθ-regular. We discuss the problem when a (countably)θ-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of aθ-regular space. Some applications: A space is paracompact iff the space is countablyθ-regular and semiparacompact. A generalizedFσ-subspace of a paracompact space is paracompact iff the subspace is countablyθ-regular.

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.

2-dimensional minkowski planes and desarguesian derived affine planes

1990 ◽  
Vol 60 (1) ◽  
pp. 61-69 ◽  
Author(s):  
G. F. Steinke
Keyword(s):  
Affine Planes ◽  
Minkowski Planes

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 ONE-POINT EXTENSIONS AND LOCAL TOPOLOGICAL PROPERTIES

2012 ◽  
Vol 88 (1) ◽  
pp. 12-16 ◽  
Author(s):  
M. R. KOUSHESH
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
General Question ◽  
Dense Subspace ◽  
Topological Properties ◽  
Locally Compact ◽  
Point Extension ◽  
One Point Compactification

AbstractA space $Y$ is called an extension of a space $X$ if $Y$ contains $X$ as a dense subspace. An extension $Y$ of $X$ is called a one-point extension of $X$ if $Y\setminus X$ is a singleton. P. Alexandroff proved that any locally compact non-compact Hausdorff space $X$ has a one-point compact Hausdorff extension, called the one-point compactification of $X$. Motivated by this, Mrówka and Tsai [‘On local topological properties. II’, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.19 (1971), 1035–1040] posed the following more general question: For what pairs of topological properties ${\mathscr P}$ and ${\mathscr Q}$ does a locally-${\mathscr P}$ space $X$ having ${\mathscr Q}$ possess a one-point extension having both ${\mathscr P}$ and ${\mathscr Q}$? Here, we provide an answer to this old question.

Generators of Monothetic Groups

1971 ◽  
Vol 23 (5) ◽  
pp. 791-796 ◽  
Author(s):  
D. L. Armacost
Keyword(s):  
Topological Group ◽  
Cyclic Subgroup ◽  
Topological Properties ◽  
Locally Compact ◽  
Separation Axiom ◽  
Lca Groups

A topological group G is called monothetic if it contains a dense cyclic subgroup. An element x of G is called a generator of G if x generates a dense cyclic subgroup of G. We denote by E(G) the set of generators of G; the complement of E(G) in G, consisting of the “non-generators” of G, we write as N(G) Throughout this paper we consider only locally compact abelian (LCA) groups satisfying the T2 separation axiom (note that a monothetic group is automatically abelian). In [1] certain problems of measurability concerning the set E(G) are discussed. In this paper we shall consider some algebraic and topological properties of the sets E(G) and N(G)

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 A generalization of the m-topology on C(X) finer than the m-topology

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2509-2515
Author(s):  
F. Azarpanah ◽  
F. Manshoor ◽  
R. Mohamadian
Keyword(s):  
Topological Properties ◽  
Compact Sets ◽  
Empty Interior ◽  
Topological Ring ◽  
Locally Compact ◽  
Regular Elements ◽  
Zero Function ◽  
The Ideal

It is well known that the component of the zero function in C(X) with the m-topology is the ideal C?(X). Given any ideal I ? C?(X), we are going to define a topology on C(X) namely the mI-topology, finer than the m-topology in which the component of 0 is exactly the ideal I and C(X) with this topology becomes a topological ring. We show that compact sets in C(X) with the mI-topology have empty interior if and only if X n T Z[I] is infinite. We also show that nonzero ideals are never compact, the ideal I may be locally compact in C(X) with the mI-topology and every Lindel?f ideal in this space is contained in C?(X). Finally, we give some relations between topological properties of the spaces X and Cm(X). For instance, we show that the set of units is dense in Cm(X) if and only if X is strongly zero-dimensional and we characterize the space X for which the set r(X) of regular elements of C(X) is dense in Cm(X).

scholarly journals On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
I. Akbarbaglu ◽  
S. Maghsoudi
Keyword(s):  
Convex Space ◽  
Topological Algebra ◽  
Locally Convex Space ◽  
Locally Compact Group ◽  
Compact Groups ◽  
Topological Properties ◽  
Locally Compact ◽  
The Family ◽  
Locally Convex Topology ◽  
Locally Convex

Let be a locally compact group with a fixed left Haar measure and be a system of weights on . In this paper, we deal with locally convex space equipped with the locally convex topology generated by the family of norms . We study various algebraic and topological properties of the locally convex space . In particular, we characterize its dual space and show that it is a semireflexive space. Finally, we give some conditions under which with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum.

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