  A new generalisation of the notion of space, called "vectoid", is suggested
in this work. Basic definitions, examples and properties are presented, as well
as a construction of direct product of vectoids. Proofs of more complicated
properties not used later are just sketched. Classifying vectoids of simplest
algebraic structures, such as objects, algebras and coalgebras, are studied in
some detail afterwards. Apart from giving interesting examples of vectoids not
coming from spaces known before (such as ringed topoi), monoids in the
endomorphism categories of these classifying vectoids turn out to provide a
systematic approach to construction of different versions of the notion of an
operad, as well as its generalisations, unknown before.
