Complete Topological Space Research Articles

On related fixed points in two d-complete topological spaces

Abstract In this paper, using the method of Hicks, we prove some new related fixed point theorems for pair of mappings on two d-complete topological spaces under the suitable conditions. We also derive some related fixed point theorems from our main results. Finally, by using w-continuity, we establish a related fixed point theorem in d-complete Hausdorff topological spaces.

The Results of Common Fixed Points in b-Metric Spaces

In this paper, we present some results on the existence and uniqueness of common fixed points on d*-complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in lp spaces, (p∈(0,1)), where we use the obtained results.

SOME FIXED POINT RESULTS IN d-COMPLETE TOPOLOGICAL SPACES

This paper aims to use T-orbitally lower semi-continuous and $w$-continuous functions in $d$-complete topological spaces to validate some fixed point theorems and extend various known results. The paper also seeks to establish, in the setting of $d$-complete topological spaces, Mizoguchi-Takahashi's type coincidence point theorem for single valued map. The results are supported by illustrative examples.

On d*-Complete Topological Spaces and Related Fixed Point Results

In this paper, we introduce the concept of d*-complete topological spaces, which include earlier defined classes of complete metric spaces and quasi b-metric spaces. Further, we prove some fixed point results for mappings defined on d*-complete topological spaces, generalizing earlier results of Tasković, Ćirić and Prešić, Prešić, Bryant, Marjanović, Yen, Caccioppoli, Reich and Bianchini.

On Suprememum of a set in A Dedikind Complete Topological Space

The supremum for a set in a multi-dimensional, Dedikind complete topological space is defined. The example is given to illustrate that the condition of Dedilind complete is necessary for the existence of supremum.

Fixed points of self maps in dp – complete topological spaces

The purpose of this paper is to prove some fixed point theorems in dp complete topological spaces which generalize the results of Troy L Hicks and B.E.Rhoades[6 ].

The Space of Coefficients in a Linear Topological Space

It is proved that the arbitrary nondegenerate system in a linear complete topological space has a correspondence complete topological space of coefficients with canonical basis. Basicity criterion for systems in such spaces is given in terms of coefficient operator.

Common coupled fixed point theorems in $d$-complete topological spaces

In this paper, we give two unique common coupled xed point the- orems for mappings satisfying a generalized condition in d-complete topological spaces.

Sums and products of ultracomplete topological spaces

In 1987 V.I. Ponomarev and V.V. Tkachuk characterized strongly complete topological spaces as those spaces which have countable character in their Stone–Čech compactification. On the other hand, in 1998 S. Romaguera introduced the notion of cofinally Čech complete spaces and he showed that a metrizable space admits a cofinally complete metric (otherwise, called ultracomplete metric), a term introduced independently by N.R. Howes in 1971 and A. Császár in 1975, if and only if it is cofinally Čech complete. In a recent paper the authors showed that these two notions are equivalent and in this way answered a question raised by Ponomarev and Tkachuk [Vestnik MGU 5 (1987) 16–19] about giving an internal characterization for strongly complete topological spaces (termed ultracomplete by the authors). In this paper, sums and products of ultracomplete spaces are studied.

Ultracomplete Topological Spaces

In 1987 V. I. Ponomarev and V. V. Tkachuk characterized strongly complete topological spaces as those spaces which have countable character in their Stone-Cech compactification. On the other hand, in 1998 S. Romaguera intro- duced the notion of cofinally Cech complete spaces and he showed that a metriz- able space admits a cofinally complete metric (otherwise called ultracomplete metric), a term introduced independently by N.R. Howes in 1971 and A. Csaaszar in 1975, if and only if it is cofinally Cech complete. In this paper we show that these two notions are equivalent and in this way answer a question raised in [16] about giving an internal characterization for strongly complete topological spaces.

Symbolic dynamics analysis of topological entropy and its multifractal structure.

By means of symbolic dynamics, we establish an expression determining the topological entropy of a Derrida-Gervois-Pomeau (DGP) compound sequence, the concept of an equal topological entropy class, and we find a global regularity in interval dynamics---the devil's staircase of topological entropy, which possesses a fractal structure and a rigorous subinterval similarity. An important result is that the bifurcation processes (period-doubling or period-n-tupling) are all processes preserving topological entropy. We also discuss the uniform compressibility of the operator Q * and the nonuniform compressibility in a series of stair-climbing sequences. Finally, we suggest a classification of all admissible words in the complete topological space ${\mathrm{\ensuremath{\Sigma}}}_{2}$ of two symbols.

Sums and products ofBrspaces

In reminiscence of Ptak's open mapping theorem, a topological space satisfying the open mapping theorem is called a Br space. This paper is devoted to the study of sums and products of Br spaces in the category of topological spaces. We prove that, in general, sums and products of even two Br spaces need no longer be Br. On the other hand, for any Br space E the sum E θ E is again a Br space. Moreover, since Cech complete spaces are known to be Br, we ask whether a sum E θ F is Br provided that E is Cech complete and F is Br. It turns out that, at least in the framework of complete regularity, the answer to this question is in the positive if and only if F is a Baire space. Introduction. The notion of Br spaces has first been introduced by T. Husain in the categories of locally convex vector spaces (see (HuJ) and topological groups (see (Hu2)). Originally, it goes back to V. Ptak's open mapping theorem (see (Kό), p. 35 ff). A Hausdorff topological space E is called a Br space if every continuous, nearly open bijection / from E onto any Hausdorff space F is in fact open. For a survey of the classical theory of Br spaces we refer the reader to Kόthe's book (Kό), where the locally convex case is treated. The linear topological case is investigated in the lecture notes (AEK). Br groups are considered by several authors. See for instance (Hu2), (Ba), (Gr), (Su). In a purely topological context, Br spaces have first been investigated by Weston in (We), although the term Br space is not used there. Translated into the Br terminology, Weston proved that every completely metrizable topological space is a Br space. His result has been generalized by Byczkowski and Pol in (BP), who proved that every Cech complete topological space is a Br space. In (No) we have further generalized this result proving that every Hausdorff, semi-regular topological space densely containing some Cech complete sub space is in fact a Br space. We just mention another generalization of Byczkowski and Pols' result into a somewhat different direction by Wilhelm (cf. (Wi)). In the present paper we examine the invariance of the class of Br spaces under topological sums and products. It turns out that, in general, the sum of even two Br spaces need not be a Br space. A counterexample is given in §2. In §1 we obtain a positive result stating that the sum E θ E

Zero-set ultrafilters and Gδ-closures in uniform spaces

AbstractThe paper examines the classes K1 and Γ1 of Hausdorff uniform spaces which are Gδ-closed in their Samuel compactifications, or completions. It is shown that the classes are epi-reflective, the reflections K1 and Γ are described, K1 and Γ1 are represented as epi-reflective hulls, membership in the classes is described by fixation of certain zero-set ultrafilters, and it is shown that k1 = Γ1 exactly on spaces without discrete sets of measurable power. The results include familiar facts about realcompact and topologically complete topological spaces and are closely connected with the theory of metric-fine uniform spaces.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 50, 54 E 15, 18 A 40; secondary 54 B 05, 54 B 10, 54 C 10, 54 C 30.