What are the fields of mathematics related with semantics technologies and their specifications as RDF, OWL, SPARQL?
If somebody working as a programmer with those technologies (using them with a practical scope and from a pragmatic point of view) would like to deepen into their mathematical aspects which reads would you recommend?
Is mathematical lattices theory related? Is topology related?
Since OWL is a description logic, the most relevant branch of mathematics for understanding OWL is logic. Graph theory, lattice theory, and topology are not very relevant (although there are some connections).
Description logics lie between propositional logic and first-order predicate logic. Learning about the syntax and semantics of these two fundamental logical systems will be helpful as background knowledge. This material is covered in any introductory logic textbook.
The book Foundations of Semantic Web Technologies explains the semantics of RDF and OWL in greater mathematical detail than is typical for books about the Semantic Web. For still greater detail, you might look at the Description Logic Handbook (the second edition contains a chapter on OWL). The textbook Knowledge Representation and Reasoning by Brachman and Levesque surveys the whole field of knowledge representation, including description logic.
From what I can gather, RDF is a query language used for databses. RDF has, as has many other modern programming languages, a formal syntax and semantics that a precise description of how the programming language works, so that no program written in the language can be ambiguous.
The syntax of a language defines what symbols and combinations of symbols are valid in the language. The semantics of the language describes what the meaning of different syntactical constructions are. To understand at a very basic level what syntax and semantics are, and why they are necessary, I would recommend a book on (propositonal) logic.
In computer science and programming languages, we often need more complicated expressions than the ones used in logic. Therefore the theory of semantics has been extended in various ways, and the two most used types of semantics today are probably denotational semantics and operational semantics (see more here).
Some related areas are automata theory, since this is very closely related to syntax of formal languages, lattice theory, since many programming languages allow for recursion, and this often requires use of fixed point theorems from lattice theory, and type theory, since a strong type system can often help to make a programming language more robust.
