Nearly prime subsemigroups of ßN.
In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.
For Tychonoff and an infinite cardinal, let the minimum number of cozero-sets of the Čech-Stone compactification which intersect to (generalizing -defect), and let . Give the compact-open topology. It is shown that , where: is tightness; is the network character; is the Lindel"of number. For example, it follows that, for Čech-complete, . The (apparently new) cardinal functions and are compared with several others.
Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space of Maass forms with eigenvalue on a congruence subgroup . We introduce the field so that consists entirely of algebraic numbers if .The main result of the paper is the following. For a packet of Hecke eigenvalues occurring in we then have that either every is algebraic over , or else will – for some – occur in the first cohomology of a certain space which is a...