Can any one tell me how the elements of the set $A^{∧∨}$ will look like? I believe they are of the following form:
$∨^m_i∧^{m_i}_{k_i} x_{i,{k_i}}$ where $x_{i,{k_i}}$ is in $A$. But in this case I'm unable to show that their union $(∨^m_i∧^{m_i}_{k_i} x_{i,{k_i}})$ ∨ $(∨^n_j∧^{n_j}_{l_j} y_{j,{l_l}})$ is in $A^{∧∨}$. Or, for negative scalar $\alpha$, how to show that $\alpha (∨^m_i∧^{m_i}_{k_i} x_{i,{k_i}})$ is in $A^{∧∨}$? 
2025-01-13 07:55:25.1736754925
General form of elements in the vector lattice (Riesz Space) generated by a vector space
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