Embedding the bicyclic semigroup into countably compact topological semigroups

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that a topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonoff semigroup containing a copy of C(p,q).     

Causal compactification and Hardy spaces

Let be a irreducible symmetric space of Cayley type. Then is diffeomorphic to an open and dense -orbit in the Shilov boundary of . This compactification of is causal and can be used to give answers to questions in harmonic analysis on . In particular we relate the Hardy space of to the classical Hardy space on the bounded symmetric domain . This gives a new formula for the Cauchy-Szegö kernel for .

     

Continuity in G

For a discrete group G, we consider βG, the Stone– ech compactification of G, as a right topological semigroup, and G^*=βGG as a subsemigroup of βG. We study the mappings λ_p^* :G^*→G^*and μ^* :G^*→G^*, the restrictions to G^* of the mappings λ_p :βG→βG and μ :βG→βG, defined by the rules λ_p(q)=pq, μ(q)=qq. Under some assumptions, we prove that the continuity of λ_p^* or μ^* at some point of G^* implies the existence of a P-point in ω^*.     

Hemiring-homomorphisms,Stone Čech Compactification and Hewitt Realcompactification

In this paper the Stone-ech Compactification and Hewitt Realcompactification of a Tychonoff space X are shown as the spaces of Hemiring Homomorphisms from the hemirings C^*₊(X) and C₊(X) to IR₊ respectively.AMS Subject Classification: 2000, 54E25     

Fundamental group of locally symmetric varieties

We investigate the fundamental group of a compactified locally symmetric variety after resolution of singularities. We show that it can be any finite group and give examples to show that even for Siegel modular threefolds it can be complicated. We also calculate some cases of special interest, including the fundamental group of the Barth-Nieto space. This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991.     

The Mardesic factorization theorem for extension theory and c-separation

We shall prove a type of Mardesic factorization theorem for extension theory over an arbitrary stratum of CW-complexes in the class of arbitrary compact Hausdorff spaces. Our result provides that the space through which the factorization occurs will have the same strong countability property (e.g., strong countable dimension) as the original one had. Taking into consideration the class of compact Hausdorff spaces, this result extends all previous ones of its type. Our factorization theorem will simultaneously include factorization for weak infinite-dimensionality and for Property C, that is, for C-spaces.

A corollary to our result will be that for any weight and any finitely homotopy dominated CW-complex , there exists a Hausdorff compactum with weight and which is universal for the property and weight . The condition means that for every closed subset of and every map , there exists a map which is an extension of . The universality means that for every compact Hausdorff space whose weight is and for which is true, there is an embedding of into .

We shall show, on the other hand, that there exists a CW-complex which is not finitely homotopy dominated but which has the property that for each weight , there exists a Hausdorff compactum which is universal for the property and weight .

     

A Constructive Proof of the Gelfand—Kolmogorov Theorem

A construction of the Stone—ech compactification of a locale L is presented in this paper as a quotient of the frame of radical ideals of the algebra C ^*(L). As a corollary, a constructive, localic version of the Gelfand—Kolmogorov theorem is obtained.     

M‐theory and gauged supergravities

We present a pedagogical discussion of the emergence of gauged supergravities from M‐theory. First, a review of maximal supergravity and its global symmetries and supersymmetric solutions is given. Next, different procedures of dimensional reduction are explained: reductions over a torus, a group manifold and a coset manifold and reductions with a twist. Emphasis is placed on the consistency of the truncations, the resulting gaugings and the possibility to generate field equations without an action. Using these techniques, we construct a number of gauged maximal supergravities in diverse dimensions with a string or M‐theory origin. One class consists of the CSO gaugings, which comprise the analytic continuations and group contractions of SO(n) gaugings. We construct the corresponding half‐supersymmetric domain walls and discuss their uplift to D‐ and M‐brane distributions. Furthermore, a number of gauged maximal supergravities are constructed that do not have an action.