The dimension Dind of finite topological T0-spaces
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Dimitrios N. Georgiou
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Yasunao Hattori
Abstract
A. V. Arhangelskii introduced the dimension Dind and properties of this dimension have been studied for various classes of topological spaces. In this paper, we study this dimension for finite T0-spaces. Especially, we prove that in the realm of finite T0-spaces, Dind is less than or equal to the small inductive dimension ind, the large inductive dimension Ind and the covering dimension dim. We also study the “gaps” between Dind and the dimensions ind, Ind and dim, presenting various examples which shows these “gaps”. Moreover, in this field of spaces, we give characterizations of Dind, inserting the meaning of the maximal family of pairwise disjoint open sets, and study properties of this dimension.
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(Communicated by L'ubica Holá)
Acknowledgement
The authors would like to thank the referee for very thorough report and for helpful comments that have improved the quality of this paper.
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Artikel in diesem Heft
- Regular Papers
- The poset of morphism-extension classes of countable graphs
- Characterization of monadic BL-algebras by state operators
- Comments on efficient batch verification test for digital signatures based on elliptic curves
- On necessary and sufficient conditions for the monogeneity of a certain class of polynomials
- An exponential Diophantine equation involving the sum or difference of powers of two Pell numbers
- Some results on certain types of Putcha semigroups
- Inner functions in QK spaces and multipliers
- Certain subclasses of meromorphic multivalent q-starlike and q-convex functions
- Algebraic dependences of meromorphic mappings into a projective space sharing few hyperplanes
- Unbounded oscillation criteria for fourth order neutral differential equations of non-canonical type
- Existence of radial solutions for a weighted p-biharmonic problem with navier boundary condition on the Heisenberg group
- Intuitionistic fuzzy Tribonacci I-convergent sequence spaces
- Lipschitz class functions and their general Fourier coefficients
-
Spectra and fine spectra of the generalized upper difference operator with triple repetition
- A Topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere
- An extended type I half-logistic family of distributions: Properties, applications and different method of estimations
- On the Unit-Chen distribution with associated quantile regression and applications
- A note on Lévy subordinators in cones of fuzzy sets in Banach spaces
- Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors
- Upper bound for variance of finite mixtures of power exponential distributions
- The dimension Dind of finite topological T0-spaces
