BCI systems analyze the EEG signal and translate patient intentions into simple commands. Signal processing methods are very important in such systems. Signal processing covers: preprocessing, feature extraction, feature selection and classification. In the article authors present the results of implementing linear discriminant analysis as a feature reduction technique for BCI systems. Streszcz...

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Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions onX which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone–Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuo...

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...

Eric van Douwen [5] produced a maximal crowded extremally disconnected regular space and showed that its Čech–Stone compactification is an at most two-to-one image of βN. We construct for any n = 3 an example of a compact crowded space Xn that is an image of βN under a map all of whose fibers have either size n or n− 1. We also show that under CH this is best possible.

We use the insights of Robinson’s nonstandard analysis as a powerful tool to extend and simplify the construction of compactifications of regular spaces. In particular, we deal with the Stone-Čech compactification and compactifications formed from topological ends. For the nonstandard extension of a metric space, the monad of a standard point x is the set of all points infinitesimally close to ...