following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of intergalactic medium (IGM) based on Voigt profile decomposition Ly α forest into set discrete absorption lines with Doppler parameter b neutral hydrogen column $N_{\rm I}}$. Previous ...

<p style='text-indent:20px;'>In this paper we study the Riemann-Liouville fractional integral of order <inline-formula><tex-math id="M1">\begin{document}$ \alpha>0 $\end{document}</tex-math></inline-formula> as a linear operator from id="M2">\begin{document}$ L^p(I,X) into itself, when id="M3">\begin{document}$ 1\leq p\leq \infty $\end{document}</te...

The thermal state of the intergalactic medium (IGM) contains vital information about epoch reionization, one most transformative yet poorly understood periods in young universe. This is encoded small-scale structure Lyman-$\alpha$ (Ly$\alpha$) absorption quasar spectra. 1D flux power spectrum measures average along sightlines. At high redshifts, where opacity large, averaging mixes signal-to-no...

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...