scholarly journals On Topological Properties of Metrics Defined via Generalized “Linking Construction”

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Marcin Borkowski ◽  
Dariusz Bugajewski ◽  
Adam Burchardt
Keyword(s):  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Necessary And Sufficient

We analyze topological properties of metric spaces obtained by using Száz’s construction, which we used to call generalized “linking construction.” In particular, we provide necessary and sufficient conditions for completeness of metric spaces obtained in this way. Moreover, we examine the relation between Száz’s construction and the “linking construction.” A particular attention is drawn to the “floor” metric, the analysis of which provides some interesting observations.

scholarly journals On topological properties of the Hausdorff fuzzy metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1167-1173
Author(s):  
Changqing Li ◽  
Kedian Li
Keyword(s):  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Necessary And Sufficient

In the paper, necessary and sufficient conditions for two Hausdorff fuzzy metric spaces to be homeomorphic are studied. Also, several properties of the Hausdorff fuzzy metric spaces, as F-boundedness, separability and connectedness are explored.

SOME TOPOLOGICAL RESULTS ON LEVEL SETS AND MULTIFRACTAL SETS

Fractals ◽  
2019 ◽  
Vol 28 (01) ◽  
pp. 2050009
Author(s):  
CHUNTAI LIU
Keyword(s):  
Level Sets ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Symbolic Space ◽  
Necessary And Sufficient

In this paper, we study topological properties of some level sets and some multifractal sets induced by Rademacher’s series and Takagi’s series, respectively. By using symbolic space, we obtain necessary and sufficient conditions for them to be residual.

On Janowski harmonic functions

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Janowski Functions ◽  
Distortion Theorems ◽  
Necessary And Sufficient

AbstractIn this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.

scholarly journals Further results on images of metric spaces

2015 ◽  
Vol 98 (112) ◽  
pp. 179-191
Author(s):  
Van Dung
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Continuous ◽  
Locally Separable Metric Spaces ◽  
Necessary And Sufficient ◽  
Separable Metric Space

We introduce the notion of an ls-?-Ponomarev-system to give necessary and sufficient conditions for f:(M,M0) ? X to be a strong wc-mapping (wc-mapping, wk-mapping) where M is a locally separable metric space. Then, we systematically get characterizations of weakly continuous strong wc-images (wc-images, wk-images) of locally separable metric spaces by means of certain networks. Also, we give counterexamples to sharpen some results on images of locally separable metric spaces in the literature.

scholarly journals On the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

On Weak Asymptotic Periodicity

2020 ◽  
Vol 30 (02) ◽  
pp. 2050030
Author(s):  
Karol Gryszka
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Property ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Conjugacy ◽  
Asymptotic Periodicity ◽  
Necessary And Sufficient

We introduce the asymptotic property associated with recurrence-like behavior of orbits in dynamical systems in general metric spaces. We define a notion of weak asymptotic periodicity and determine its elementary properties and relations including the invariance by topological conjugacy. We use the equicontinuity and the topology of the space to describe necessary and sufficient conditions for the existence of such a behavior.

Characterizations of Spherical Neighbourhoods

1970 ◽  
Vol 22 (2) ◽  
pp. 431-435 ◽  
Author(s):  
C. M. Petty ◽  
J. M. Crotty
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Characterization Problem ◽  
Necessary And Sufficient

If Σ is a specified class of metric spaces and M ∈ Σ, then the characterization problem is to find necessary and sufficient conditions which distinguish the spherical neighbourhoods (open spheres) of M among a specified class of subsets of M.In a metric space M the notation pqr means p ≠ q ≠ r and pq + qr = pr.M is said to be uniformly locally externally convex if there exists δ > 0 such that if p, q ∈ M, p ≠ q, and pq < δ, then there exists r ∈ M such that the relation pqr subsists. We will prove the following result.

scholarly journals Common stationary points of multivalued mappings on bounded metric spaces

2000 ◽  
Vol 24 (11) ◽  
pp. 773-779 ◽  
Author(s):  
Zeqing Liu ◽  
Shin Min Kang
Keyword(s):  
Stationary Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stationary Points ◽  
Multivalued Mappings ◽  
Necessary And Sufficient

Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta and Nikaido in 1994.

Topological Properties of a Class of Higher-dimensional Self-affine Tiles

2019 ◽  
Vol 62 (4) ◽  
pp. 727-740
Author(s):  
Guotai Deng ◽  
Chuntai Liu ◽  
Sze-Man Ngai
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Higher Dimensional ◽  
Necessary And Sufficient

AbstractWe construct a family of self-affine tiles in $\mathbb{R}^{d}$ ($d\geqslant 2$) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in $\mathbb{R}^{2}$, and its extension to $\mathbb{R}^{3}$ by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.

scholarly journals On Conditions for Unrectifiability of a Metric Space

2014 ◽  
Vol 3 (1) ◽  
Author(s):  
Piotr Hajłasz ◽  
Soheil Malekzadeh
Keyword(s):  
Metric Space ◽  
Implicit Function Theorem ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Implicit Function ◽  
Heisenberg Groups ◽  
Lipschitz Map ◽  
Necessary And Sufficient

Abstract We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.

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