Influence of ideals in compactifications
-
Manoranjan Singha
and
Sima Roy
Abstract
One point compactification is studied in the light of ideal of subsets of ℕ. 𝓘-proper map is introduced and showed that a continuous map can be extended continuously to the one point 𝓘-compactification if and only if the map is 𝓘-proper. Nowhere tallness, introduced by P. Matet and J. Pawlikowski in [J. Symb. Log. 63(3) (1998), 1040–1054], plays an important role in this article to study various properties of 𝓘-proper maps. It is seen that one point 𝓘-compactification of a topological space may fail to be Hausdorff even if the underlying topological space is Hausdorff but a class {𝓘} of ideals has been identified for which one point 𝓘-compactification coincides with the one point compactification if the underlying topological space is metrizable. Let’s speak our minds that the results in this article will look elegant if one looks at it from a topological angle.
The work of Ms. S. Roy has been supported by CSIR(Ref: 17/12/2017(ii)EU-V (CSIR-UGC NET DEC, 2017)), India
Acknowledgement
The authors would like to express their sincere gratitude to the anonymous referee for giving expertise comments and valuable suggestions which improved the presentation of the paper.
Communicated by L’ubica Holá
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Articles in the same Issue
- On the Paley graph of a quadratic character
- A topological duality for tense modal pseudocomplemented De Morgan algebras
- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
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- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
- On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
- Positive bases, cones, Helly-type theorems
- Digital Jordan surfaces arising from tetrahedral tiling
- Influence of ideals in compactifications
- On the functions ωf and Ωf
- On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
- A bivariate distribution with generalized exponential conditionals
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