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Wikipedia states:

The least and greatest element of the whole partially ordered set plays a special role and is also called bottom and top, or zero (0) and unit (1), or ⊥ and ⊤, respectively. If both exists, the poset is called a bounded poset.

Greatest and least elements of a partially ordered set does not always exist but if they exist then they are unique and based on this link maximal and minimal of this set are are also unique, I'm wondering if these terminologies bottom and top are the synonyms of minimum and maximum of the partially ordered set respectively.

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$\top$ and $\bot$ are symbols for the maximum and the minimum element of the poset respectively.

Most of the time, these symbols are used for boolean algebras (remember that the relation $x \leqslant y : \Leftrightarrow xy = x$ defines a partial order on a boolean algebra). There, $\top$ and $\bot$ (resp.) correspond to the $1$ and $0$ of the algebra. These symbols were chosen because they correspond (resp.) to the tautology and the antilogy.

Olivier Roche
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  • so a bounded poset is a set that has its top and bottom or equivalently it contains its maximum and minimum resp? –  Feb 06 '20 at 16:11
  • @user715522 Yes. I would say "has a maximal element" because if you say "contains its maximum" then you implicitly assume that this maximum is given by the context. – Olivier Roche Feb 06 '20 at 17:24