**Space of notion. Detailed and curtailed form of presentation.**
Notion – is an area of notion space, it could be determined as a number of atom features, each of them is a section on co-ordinate hub, measuring semantic space.
That’s is to say, notion could be presented as two vectors. The first of which is a number of co-ordinates of *hyperflatness*, reflected minimal *co-ordinate value* of this notion’s area bounds. The second is number of co-ordinate of hyperflatness, which limits maximum value of the same co-ordinates (“upper” hyperflatness).
N={N_{min}, N_{max}} or
N={N{x_{1}, x_{2}, …, x_{n}}, N{x_{1’}, x_{2’}, …, x_{n’}} or
N{{x_{1}, x_{1’}}, {x_{2}, x_{2’}}, …, |{x_{n}, x_{n’}}|}, N – is a n-dimensioned are in n-dimension space, nε∞, {1, …n} – are dimensions (co-ordinate hubs) of this space, x_{1}, x_{2}, …, x_{n} – are co-ordinates of lower hyperflatness’s area of space, x_{1’}, x_{2’}, …, x_{n’} – are co-ordinates of upper hyperflatness’s area of space.
Expressions, presented earlier, determine detailed form of notion space presentation. However, practically most part of co-ordinates x_{n}=x_{n’} (for objects), |x_{n}-x_{n’} |ε0. that is to say, projection of concrete multi-dimension area to some *dimension* is nominal (that means, that this notion at this context hasn’t got a sense). Hence, for calculations and measuring this dimension for notion is considered to be degenerated, empty, curtailed. Co-ordinate data collated to this dimension considered to be zero in calculations. If this dimension is degenerated for the whole domain, it is clear, that those co-ordinates could be left out, noting in what domain calculations are held.
For enlarging approach could be said that totally notion space is a space with variable *dimension. *However, for each concrete area of semantic space, correlated to certain domain (object area), finite number of dimensions and its constancy could be accepted.
Thus, curtailed of *estimated* form of notion space presentation will be:
N={N_{min}, N_{max}} or
N={N{x_{1}, x_{2}, …, x_{k}}, N{x_{1’}, x_{2’}, …, x_{k’}} or
N{{x_{1}, x_{1’}}, {x_{2}, x_{2’}}, …, |{x_{k}, x_{k’}}|}, N – is a k-dimensioned are in n- dimension space, nε∞, k – is natural number, x_{1}, x_{2}, …, x_{k} – are co-ordinates of lower hyperflatness’s area of space, x_{1’}, x_{2’}, …, x_{k’} – are co-ordinates of upper hyperflatness’s area of space. Further for considerations and calculations will be used the curtailed form of notion space presentation. |