We prove that the geodesic flow on a compact locally CAT(−1) space has the weak specification property, and give various applications of this property. We show that every Hölder continuous function on the space of geodesics has a unique equilibrium state, and as a result, that the BowenMargulis measure is the unique measure of maximal entropy. We establish the equidistribution of weighted perio...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

For a continuous self mapping f of a locally convex topological vector space which is locally compact (i.e., f maps a neighborhood of each point into a relatively compact set), it is shown that a sufficient condition for the existence of a fixed point is the existence of a compact attractor K(0) such that each orbit under f has a point of K(0) in its closure. The proof is based upon the circle ...

We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolemy.

A new, more widely applicable, constructive definition of locally compact metric space is given, and a metric one-point compactification is constructed. Classically, this provides a simpler, more direct, construction of a metric on the one-point compactification of a separable locally compact metric

Completely regular pseudo-compact spaces have been characterized in several ways. E. Hewitt [6, pp. 68-70] has given one characterization in terms of the Stone-Cech compactification and another in terms of the zero sets of continuous functions. J. Colmez [2; no proofs included] and I. Glicksberg [4] have obtained characterizations by means of a convergence property for sequences of continuous f...

To determine what spaces are the images of “nice” spaces under “nice” mappings is one of the central questions of general topology in 1 . In the past, many noteworthy results on images of metric spaces have been obtained. For a survey in this field, see 2 , for example. A characterization for a quotient compact image of a locally separable metric space is obtained in 3 . Also, such a quotient i...

For any point xEX, we denote by HXEG the isotropy subgroup of G at xEX. The group G will be a compact Lie group. The space X is assumed to be locally compact, locally connected, finite dimensional and separable metric. We shall use the Alexander-Wallace-Spanier cohomology groups. A subscript c will denote cohomology with compact supports. The coefficient ring J will denote either the integers Z...

Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and s-compact. (ii) CpðXÞ is analytic. (iii) CpðXÞ is K-analytic. (iv) CpðXÞ is Lindelöf. (v) CcðX Þ is a separable metrizable and complete locally convex space. (vi) CcðX Þ is compactly dominated by irrationals. This result supplements earlier results ...

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.