A characterization of compact scattered spaces through chain limits; (chain compact spaces)

1974 ◽  
pp. 288-297 ◽  
Author(s):  
S. Mrowka ◽  
M. Rajagopalan ◽  
T. Soundararajan
Keyword(s):  
Compact Spaces ◽  
Scattered Spaces

scholarly journals On equicontinuous factors of flows on locally path-connected compact spaces

2020 ◽  
pp. 1-18
Author(s):  
NIKOLAI EDEKO
Keyword(s):  
Lie Group ◽  
Metric Space ◽  
Betti Number ◽  
Alternative Proof ◽  
Simple Consequence ◽  
Compact Metric Space ◽  
Invariant Functions ◽  
Compact Spaces ◽  
Path Connected

Abstract We consider a locally path-connected compact metric space K with finite first Betti number $\textrm {b}_1(K)$ and a flow $(K, G)$ on K such that G is abelian and all G-invariant functions $f\,{\in}\, \text{\rm C}(K)$ are constant. We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than ${\textrm {b}_1(K)}/{\textrm {b}_0(K)}$ . For this purpose, we use and provide a new proof for Theorem 2.12 of Hauser and Jäger [Monotonicity of maximal equicontinuous factors and an application to toral flows. Proc. Amer. Math. Soc.147 (2019), 4539–4554], which states that for a flow on a locally connected compact space the quotient map onto the maximal equicontinuous factor is monotone, i.e., has connected fibers. Our alternative proof is a simple consequence of a new characterization of the monotonicity of a quotient map $p\colon K\to L$ between locally connected compact spaces K and L that we obtain by characterizing the local connectedness of K in terms of the Banach lattice $\textrm {C}(K)$ .

scholarly journals A characterization of $N$-compact spaces

1970 ◽  
Vol 26 (4) ◽  
pp. 679-679
Author(s):  
Kim-peu Chew
Keyword(s):  
Compact Spaces

A Characterization of N-Compact Spaces

1970 ◽  
Vol 26 (4) ◽  
pp. 679 ◽  
Author(s):  
Kim-Peu Chew
Keyword(s):  
Compact Spaces

Characterization of the shapes of compact spaces with the aid of the spectra of their nerves of coverings

1979 ◽  
Vol 20 (1) ◽  
pp. 92-100
Author(s):  
I. S. Rubanov
Keyword(s):  
Compact Spaces

scholarly journals On Hausdorff compactifications of non-locally compact spaces

1979 ◽  
Vol 2 (3) ◽  
pp. 481-486
Author(s):  
James Hatzenbuhler ◽  
Don A. Mattson
Keyword(s):  
Hausdorff Space ◽  
Locally Compact ◽  
Completely Regular ◽  
Compact Spaces ◽  
Hausdorff Compactifications ◽  
Set Of Points ◽  
Locally Compact Spaces

LetXbe a completely regular, Hausdorff space and letRbe the set of points inXwhich do not possess compact neighborhoods. AssumeRis compact. IfXhas a compactification with a countable remainder, then so does the quotientX/R, and a countable compactificatlon ofX/Rimplies one forX−R. A characterization of whenX/Rhas a compactification with a countable remainder is obtained. Examples show that the above implications cannot be reversed.

The numerical range of functions and best approximation

1974 ◽  
Vol 76 (1) ◽  
pp. 133-141 ◽  
Author(s):  
Lawrence A. Harris
Keyword(s):  
Convex Hull ◽  
Linear Space ◽  
Best Approximation ◽  
Normed Linear Space ◽  
Numerical Range ◽  
Closed Convex Hull ◽  
Compact Spaces ◽  
Range Of Functions ◽  
Function Mapping

In this note, we state general conditions which imply that the numerical range of a function mapping a set S into a normed linear space Y is the closed convex hull of the spatial numerical range of the function. This conclusion is of interest since, for example, it is equivalent to an extension to non-compact spaces of Kolmogoroff's characterization of functions of best approximation.

A Characterization of C-Compact Spaces

1981 ◽  
Vol 82 (4) ◽  
pp. 657
Author(s):  
Jesse P. Clay ◽  
James E. Joseph
Keyword(s):  
Compact Spaces

Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces

2015 ◽  
Vol 4 (2) ◽  
pp. 47-55 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Linear Space ◽  
Linear Operators ◽  
Vector Spaces ◽  
Closed Space ◽  
Normed Spaces ◽  
Topological Vector Spaces ◽  
Compact Spaces ◽  
Inverse Theorems ◽  
Fuzzy Vector

In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy a-Cauchy sequence of fuzzy points and fuzzy completeness.

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.

Profinite multiplicativity of functors and characterization of projective monads in the category of compact spaces

1990 ◽  
Vol 42 (9) ◽  
pp. 1131-1134
Author(s):  
M. M. Zarichnyi
Keyword(s):  
Compact Spaces
Sign in / Sign up

Export Citation Format

Share Document