In this paper we propose a new document classification method, bridging discrepancies (so-called semantic gap) between the training set and the application sets of textual data. We demonstrate its superiority over classical text classification approa
ches, including traditional classifier ensembles. The method consists in combining a document categorization technique with a single classifier or a classifier ensemble (SEMCOM algorithm - Committee with Semantic Categorizer).
A function F:R^2->R is sup-measurable if F_f:R->R given by F_f(x)=F(x,f(x)), x in R, is measurable for each measurable function f:R->R. It is known that under different set theoretical assumptions, including CH, there are sup-measurable non-measurabl
e functions, as well as their category analog. In this paper we will show that the existence of category analog of sup-measurable non-measurable functions is independent of ZFC. A similar result for the original measurable case is a subject of a work in prepartion by Roslanowski and Shelah.
We construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f:R-->R with Cantor intermediate value property which is not almost continuous. This gives a partial answe
r to a question of D. Banaszewski. We also show that every extendable function g:R-->R with a dense graph satisfies the following stronger version of the SCIVP property: for every a<b and every perfect set K between g(a) and g(b) there is a perfect subset C of (a,b) such that g[C] subset K and g|C is continuous strictly increasing. This property is used to construct a ZFC example of an additive almost continuous function f:R-->R which has the strong Cantor intermediate value property but is not extendable. This answers a question of H. Rosen. This also generalizes Rosens result that a similar (but not additive) function exists under the assumption of the continuum hypothesis.
The goal of this note is to construct a uniformly antisymmetric function f:R-> R with a bounded countable range. This answers Problem 1(b) of Ciesielski and Larson. (See also list of problems in Thomson and Problem 2(b) from Ciesielskis survey.) A pr
oblem of existence of uniformly antisymmetric function f:R-> R with finite range remains open.
We will prove that there exists a model of ZFC+``c= omega_2 in which every M subseteq R of cardinality less than continuum c is meager, and such that for every X subseteq R of cardinality c there exists a continuous function f:R-> R with f[X]=[0,1].
In particular in this model there is no magic set, i.e., a set M subseteq R such that the equation f[M]=g[M] implies f=g for every continuous nowhere constant functions f,g:R-> R .
A function f from reals to reals (f:R->R) is almost continuous (in the sense of Stallings) iff every open set in the plane which contains the graph of f contains the graph of a continuous function. Natkaniec showed that for any family F of continuu
m many real functions there exists g:R->R such that f+g is almost continuous for every f in F. Let AA be the smallest cardinality of a family F of real functions for which there is no g:R->R with the property that f+g is almost continuous for every f in F. Thus Natkaniec showed that AA is strictly greater than the continuum. He asked if anything more could be said. We show that the cofinality of AA is greater than the continuum, c. Moreover, we show that it is pretty much all that can be said about AA in ZFC, by showing that AA can be equal to any regular cardinal between c^+ and 2^c (with 2^c arbitrarily large). We also show that AA = AD where AD is defined similarly to AA but for the class of Darboux functions. This solves another problem of Maliszewski and Natkaniec.
