# ${\Omega \choose T}\neq {\Omega \choose \Gamma}$

## TL;DR

This paper demonstrates that the selection principles ${
m oldsymbol{igOmega}race T}$ and ${
m oldsymbol{igOmega}race oldsymbol{igGamma}}$ are not equivalent by constructing a specific topological space that satisfies one but not the other, answering a previously open question.

## Contribution

It provides a concrete example of a topological space distinguishing between the principles ${
m oldsymbol{igOmega}race T}$ and ${
m oldsymbol{igOmega}race oldsymbol{igGamma}}$, resolving an open problem.

## Key findings

- Constructed a topological space satisfying ${
m oldsymbol{igOmega}race T}$ but not ${
m oldsymbol{igOmega}race oldsymbol{igGamma}}$
- Answered an open question from arXiv:math/0301011
- Showed the principles are not equivalent in general

## Abstract

We show that the selection principles ${\Omega\choose T}$ and ${\Omega\choose\Gamma}$ are not equal constructing a topological space $(X,\tau)$ that satisfies ${\Omega \choose T}$, but not ${\Omega \choose \Gamma}$. This answers a question from arXiv:math/0301011 .