It is well known that domain representable spaces, that is topological spaces which are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire. MR Clas...

The main result is the following. Let f:X→Y be a continuous mapping of completely Baire space X onto hereditary weakly Preiss-Simon regular Y such that image every open subset resolvable set in Y. Then Baire. classical Hurewicz theorem about closed embedding rational numbers into metrizable spaces generalized to spaces.

Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space. Assuming the continuum hypothesis (CH), Oxtoby [9] constructed a Baire space whose square is not Baire. We will show in this paper that the assumption of CH is unnecessary. Such results are greatly enhanced by Krom [5], who showed that if there is such an example, then there...

A space is a Bake space if the intersection of countably many dense open sets is dense. We show that if X is a non-separable completely met&able linear space (pathconnected abelian topological group) then X contains two linear subspaces (subgroups) E and F such that both E and F are Baire but E x F is not. If X is a completely met&able linear space of weight K, then X is the direct sum E@F of t...

We present several recent examples of the generic approach to nonlinear problems. In this approach, instead of considering, for instance, the convergence of an algorithm, one investigates an appropriate space of algorithms equipped with some natural complete metric and shows that convergence does indeed occur for most algorithms there. As we shall see, sometimes one can show that the complement...

We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers P not Gδ · Fσ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ P of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. T...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.