Neutrosophic αψ-Homeomorphism in Neutrosophic Topological Spaces

In this article, the concept of neutrosophic homeomorphism and neutrosophic αψ homeomorphism in neutrosophic topological spaces is introduced. Further, the work is extended as neutrosophic αψ∗ homeomorphism, neutrosophic αψ open and closed mapping and neutrosophic Tαψ space in neutrosophic topological spaces and establishes some of their related attributes.

C̆ech Fuzzy Soft Closure Spaces

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

Mapping i2 on the free paratopological groups

Let FP(X) be the free paratopological group over a topological space X. For each nonnegative integer n ? N, denote by FPn(X) the subset of FP(X) consisting of all words of reduced length at most n, and in by the natural mapping from (X ? X?1 ? {e})n to FPn(X). We prove that the natural mapping i2:(X ? X?1 d ?{e})2 ? FP2(X) is a closed mapping if and only if every neighborhood U of the diagonal ?1 in Xd x X is a member of the finest quasi-uniformity on X, where X is a T1-space and Xd denotes X when equipped with the discrete topology in place of its given topology.

Some weakly mappings on intuitionistic fuzzy topological spaces

In this paper, we shall introduce concepts of fuzzy semiopen set, fuzzy semiclosed set, fuzzy semiinterior, fuzzy semiclosure on intuitionistic fuzzy topological space and fuzzy open (fuzzy closed) mapping, fuzzy irresolute mapping, fuzzy irresolute open (closed) mapping, fuzzy semicontinuous mapping and fuzzy semiopen (semiclosed) mapping between two intuitionistic fuzzy topological spaces. Moreover, we shall discuss their some properties.

On locallys-closed spaces

In the present paper, the concepts ofs-closed sub-spaces, locallys-closed spaces have been introduced and characterized. We have seen that locals-closedness is a semi-regular property; the concept ofs-θ-closed mapping has been introduced here and the following important properties are established:-Letf:X→Ybe ans-θ-closed surjection withs-set (Maio and Noiri [8]) point inverses. Then:(a) Iffis completely continuous (Arya and Gupta [1]) andYis locally compactT2-space, then,Xis locallys-closed.(b) Iffisν-continuous (Ganguly and Basu [5]) andXis a locally compactT2-space, then,Yis locallys-closed.

On the strongly countable-dimensionality of μ-spaces

Nagata in [3] defined strongly countable-dimensional spaces which are the countable union of closed finite-dimensional subspaces. Walker and Wenner in [7] characterized such metric spaces as follows: a space X is a strongly countable-dimensional metric space if and only if there exists a finite-to-one closed mapping of a zero-dimensional metric space onto X with weak local order.

Local expansions and accretive mappings

LetXandYbe complete metric spaces withYmetrically convex, letD⊂Xbe open, fixu0∈X, and letd(u)=d(u0,u)for allu∈D. Letf:X→2Ybe a closed mapping which maps open subsets ofDonto open sets inY, and supposefis locally expansive onDin the sense that there exists a continuous nonincreasing functionc:R+→R+with∫+∞c(s)ds=+∞such that each pointx∈Dhas a neighborhoodNfor whichdist(f(u),f(v))≥c(max{d(u),d(v)})d(u,v)for allu,v∈N. Then, giveny∈Y, it is shown thaty∈f(D)iff there existsx0∈Dsuch that forx∈X\D,dist(y,f(x0))≤dist(u,f(x)). This result is then applied to the study of existence of zeros of (set-valued) locally strongly accretive andϕ-accretive mappings in Banach spaces