Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The limit this contains homeomorphic copy $X$ that is strong deformation retract. We provide method approximate the homology groups and other algebraic invariants. Finally, study computational aspects implementation method.

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

It is well-known that the construction of Zariski spectra (commutative) rings yields a dual adjunction between category and locally ringed spaces. There are many constructions algebras in various contexts giving such adjunctions. Michel Coste unified them language categorical logic by showing that, for an appropriate triple $ (T_0,T,\Lambda) (which we call spatial context), each T_0 $-model can...

We obtain the further characterizations and properties of weakly open functions in bitopological spaces due to Jelić [5]. AMS Mathematics Subject Classification (2000): 54C10, 54E55

Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity functions in IFS has iterated systems. If are contractions, then is guaranteed a unique attractor. Recently, however, there an interest what occurs attractor at boundary between contractvity expansion IFS. That subject this paper. For family $F_t...

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

We have performed X-ray diffraction experiments on a single crystalline CeCoSi to investigate the unresolved ordered phase below $T_0 \sim 12$ K. discovered that triclinic lattice distortion takes place $T_0$, which is further modified in subsequent antiferromagnetic phase. The structural domains can be selected by applying magnetic field, indicating some electronic ordering exists behind and a...