On Invariant Sets Topology

International Journal of Scientific Research in Computer Science, Engineering and Information Technology, 2017

This paper presents the topological space over fuzzy set. There are the fuzzy points. The open set is reviewed here to develop this result. The collection of subsets of the set of the topological space is generalised in this paper. The fuzzy topological space and its operation are used in fuzzy points. The order of the subset of the topological space will be even is proved also in this paper.

Demonstratio Mathematica

Given a mapping f from a finite set X n on itself, we explore the finite topology τ f defined by the stable subsets E of X n ; i.e., the subsets E of X n which satisfy f (E) ⊆ E. Necessary and sufficient conditions are found in order that a finite topology τ may correspond to the topology τ f for a certain mapping f. A number of results relating properties of topology τ f with properties of the mapping f itself are also exposed.

International journal of scientific research in computer science, engineering and information technology, 2017

This paper proposes the new contractive mapping based invariant points in topological space by the study of topological semigroup over the fixed point. This mapping is defined in metric space into itself under the new condition involved the inequality sign of less than or equal to. The continuous and equicontinuous properties are studied over the convex subset. The fixed-point properties in convex space is generalised in this paper. The reversibility of the topological semigroup is applied to propose the new invariant points.

Acta Mathematica Hungarica, 2008

We prove that the family of all invariant sets of iterated systems of contractions R N → R N is a nowhere dense Fσ type subset in the space of the non-empty compact subsets of R N equipped with the Hausdorff metric. * Supported by the Hungarian research grant No. OTKA T/17 48753.

2012

Contemporary mathematics, 2011

I survey some problems and techniques that have interested me over the years, e.g. normality vs. collectionwise normality, reflection, preservation by forcing, forcing with Souslin trees, and Lindelöf problems.

 Abstract-In this paper, we define and introduce a new type of topological transitive map called θ-transitive and investigate some of its properties in (X, τ θ),   denotes the θ–topology of a given topological space (X, τ). Further, we introduce the notions of θ-minimal mapping. We have proved that every topologically transitive map is a θ-type transitive map but the converse not necessarily true, unless the space X is regular and that every minimal map is a θ-minimal map, but the converse not necessarily true. 1. INTRODUCTION In 1943, Fomin [10] introduced the notion of θ-continuous maps. The notions of θ-open sets, θ-closed sets and θ-closure where introduced by Veliˇcko [1] for the purpose of studying the important class of H-closed spaces in terms of arbitrary fiber-bases. Dickman and Porter [2], [3], Joseph [4] and Long and Herrington [14] continued the work of Velicˇko. Recently, Jafari [6] has also obtained several new and interesting results related to these sets. For the...

Fractals, 2002

We consider the attractor T of injective contractions f 1 , · · · , f m on R 2 which satisfy the Open Set Condition. If T is connected, then T 's interior T • either is empty or has no holes, and T 's boundary ∂T is connected; if further T • is nonempty and connected, then ∂T is a simple closed curve, thus T is homeomorphic to the unit disk {x ∈ R 2 : |x| ≤ 1}.

Topology and its Applications, 1997

A space X is called a t-image of Y if C,(X) is homeomorphic to a subspace of C,(Y). We prove that if Y is a t-image of X, then Y is a countable union of images of X under almost lower semicontinuous finite-valued mappings (see Definition 1.4). It follows that if Y is a t-image of X (in particular, if X and Y are t-equivalent), then for every n E w, hl(Y") 6 hl(X"), hd(Y") < hd(X") and s(Y") < 8(X"). 0 1997 Elsevier Science B.V.

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