TY  - Type of reference 
TI  - [FORTHCOMING] Algebraic properties of subspace topologies 
AU  - Noômen Jarboui
 
AU  - Bana Al Subaiei 
AB  - It is shown that the collection of all topologies on a given set $$$X$$$ coincide with the set of subsemirings of the power set $$$\mathcal{P}(X)$$$ (equipped with union and intersection) if and only if $$$X$$$ is finite. Furthermore, given a topological space $$$(X, \mathcal{T})$$$ and a subset $$$A$$$ of $$$X$$$, we characterize when the subspace topology $$$\mathcal{T}_A$$$ is a maximal (resp., a prime) ideal of the semiring $$$\mathcal{T}$$$. As applications, we provide an algebraic characterization of the one-point compactification of a noncompact, Tychonoff space. Moreover, we describe explicitly the semiring  homomorphisms from $$$\mathcal{P}(X)$$$ into $$$\mathcal{P}(Y)$$$ in case $$$X$$$ is a finite set and $$$Y$$$ is an arbitrary nonempty set. 
DO  - TBA 
JF  - Advances in Pure and Applied Mathematics 
KW  - One-point compactification, Completely regular topological space, Semiring, Maximal ideal, One-point compactification, Completely regular topological space, Semiring, Maximal ideal,  
L1  -  
LA  - en 
PB  - ISTE OpenScience 
DA  - 2024/07/8 
SN  - 1869-6090 
TT  - [FORTHCOMING] Propriétés algébriques des sous-espaces de topologies 
UR  - https://openscience.fr/Algebraic-properties-of-subspace-topologies 
IS  - Forthcoming papers<br> 
VL  -  
ER  -