*Editors*: D. Bao (San Francisco, SFSU), D. Blecher
(Houston), B. G. Bodmann (Houston), H. Brezis (Paris and Rutgers),
B. Dacorogna (Lausanne), K. Davidson (Waterloo), M. Dugas (Baylor), M.
Gehrke (LIAFA, Paris7), C. Hagopian (Sacramento), A. Haynes (Houston), R. M. Hardt (Rice), Y. Hattori
(Matsue, Shimane), W. B. Johnson (College Station), M. Rojas (College Station),
Min Ru (Houston), S.W. Semmes (Rice).

*Managing Editors*: B. G. Bodmann and K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

The Bolzano-Weierstrass theorem in generalised analysis, pp. 1081-1109.

ABSTRACT. Let κ be an uncountable regular cardinal with κ

Counting roots of polynomials over Z/p

ABSTRACT. Until recently, the only known method of finding the roots of polynomials over prime power rings, other than fields, was brute force. One reason for this is the lack of a division algorithm, obstructing the use of greatest common divisors. Fix a prime integer p and f in (Z/p

The Nevanlinna and Valiron deficiencies of some q-difference-differential polynomials, pp. 1121-1134.

ABSTRACT. For a zero order meromorphic function f(z), the main purpose of this paper is to investigate the value distribution on f, f' and some types of q-difference-differential polynomials. We obtain some interesting results, which reveal the relation of Nevanlinna deficiencies among such functions concerning Valiron deficiency. Moreover, we give some examples to explain our conclusions.

On local holomorphic conformal embeddings, pp. 1135-1145.

ABSTRACT. We first develop some general properties for holomorphic conformal maps between Kähler manifolds, such as extension and algebraicity. Applying these properties, some rigidity results for holomorphic conformal maps from the unit disk to the product of unit balls are obtained.

Some properties of Zermelo navigation in pseudo-Finsler metrics under an arbitrary wind, pp. 1147-1179.

ABSTRACT. We generalize the notion of Zermelo navigation to arbitrary pseudo-Finsler metrics possibly defined in conic subsets. The translation of a pseudo-Finsler metric F is a new pseudo-Finsler metric whose indicatrix is the translation of the indicatrix of F by a vector field W at each point, where W is an arbitrary vector field, without the classical restriction of W being mild (i.e. we allow the opposite of W to have F-norm bigger or equal to 1). Then we show that the Matsumoto tensor of a pseudo-Finsler metric is equal to zero if and only if it is the translation of a semi-Riemannian metric, and when W is homothetic, we give a description of the geodesic flow of the translation and we prove that the flag curvature of the translation coincides with the one of the original one up to the addition of a non-positive constant. We give a proof of the latter by exploiting the fanning curve approach to the flag curvature. These results allow us to extend all the Randers spaceforms classified by D. Bao, C. Robles and Z. Shen (in J. Differential Geom., 66 (2004)) to geodesically complete conic Finsler manifolds with constant flag curvature.

On arithmetic general theorems for polarized varieties, pp. 1181-1203.

ABSTRACT. We apply Schmidt's Subspace Theorem to establish Arithmetic General Theorems for projective varieties over number and function fields. Our first result extends an analogous result of M. Ru and P. Vojta. One aspect to its proof makes use of a filtration construction which appears in work of Autissier. Further, we consider work of M. Ru and J. T.-Y. Wang which pertains to an extension of K. F. Roth's theorem for projective varieties in the sense of D. McKinnon and M. Roth. Motivated by these works, we establish our second Arithmetic General Theorem, namely a form of Roth's theorem for exceptional divisors. Finally, we observe that our results give, within the context of Fano varieties, a sufficient condition for validity of the main inequalities predicted by Vojta.

Operator space structures on ℓ

ABSTRACT. We show that the complex normed linear space ℓ¹(n) for n > 1 has no isometric embedding into complex matrices of size k for any natural number k and discuss a class of infinite-dimensional operator space structures on it.

Homological properties of some Banach modules related to completely continuous convolution operators, pp. 1213-1220.

ABSTRACT. For a locally compact group G, the notion of a Dunford-Pettis operator and the convolution product were used to introduce the function space DP(G). Closely related to this space is the space of all left uniformly measurable functions on G that denoted by LUM(G). Here, we investigate projectivity, injectivity and flatness of LUM(G) and DP(G) as Banach right modules over the group algebra.

Points of strong subdifferentiability in dual spaces, pp. 1221-1226.

ABSTRACT. In this paper, motivated by a classical results of Franchetti and Paya on points of strong subdifferentiability, we exhibit several naturally occurring situations when the property of being strongly subdifferentiable can be lifted from a subspace to the entire space. Our methods rely on the deep analysis of strongly proximinal subspaces of finite codimension done by Godefroy and Indumathi and techniques from the theory of M-ideals.

A Green-Julg isomorphism for inverse semigroups, pp. 1227-1240.

ABSTRACT. For every finite unital inverse semigroup and equivariant C*-algebra we establish a Green-Julg isomorphism between equivariant K-theory of the C*-algebra and the non-equivariant K-theory of the crossed of the C*-algebra by the inverse semigroup.

Free groups and quasidiagonality, pp. 1241-1267.

ABSTRACT. We use free groups to settle a couple questions about the values of the Pimsner-Popa-Voiculescu modulus of quasidiagonality for a set of operators Ω, denoted by qd(Ω). Along the way we deduce information about the operator space structure of finite dimensional subspaces of ℂ[𝔽

Category theoretic characterizations of generalized inverse limits, pp. 1269-1291.

ABSTRACT. We construct a category

On midpoint-free subsets of some topological groups, pp. 1293-1311.

ABSTRACT. A subset of an abelian group is midpoint-free if it contains no three distinct elements a, b, c such that a+b=2c. We study midpoint-free sets in various classical topological groups. For every infinite cardinal k not greater than the cardinality of the continuum, we show that the real line can be partitioned into k-many maximal midpoint-free sets. Examples of closed maximal midpoint-free subsets are given for topological groups such as the real line, the complex plane, the one-dimensional sphere and the torus. Finally, among sets that are not regular, such as non-measurable sets, Bernstein sets, and Luzin sets, we study instances which are midpoint-free.

Generalized set-valued inverse limits with finite coordinate spaces, pp. 1313-1334.

ABSTRACT. Generalized set-valued inverse limits whose first coordinate space is a compact metric space and all of whose subsequent spaces are finite non-Hausdorff spaces are considered. A condition is stated that causes such inverse limit spaces to be compact metric spaces. Several examples are provided and the algebraic structure is examined in the case where the resultant metric space is a topological group. The example of the solenoid as a topological group is considered in detail.

Almost meshed locally connected continua without unique n-fold hyperspace suspension, pp. 1335-1365.

ABSTRACT. For a metric continuum X and a positive integer n, we consider the hyperspaces C

On perfect images of mu-spaces, pp. 1367-1376.

ABSTRACT. A space is called a μ-space if it can be embedded in the product of countably many paracompact F

A quasitopological modification of semitopological groups, pp. 1377-1388.

ABSTRACT. In this paper, for a given semitopological group H and each positive integer n , we define a quasitopological group Q

The weak Urysohn number and upper bounds for cardinality of Hausdorff spaces, pp. 1389-1398.

ABSTRACT. In this article, following the line of research of Bonanzinga (On the Hausdorff number of a topological space, Houston J. Math. 2013) we introduce a new cardinal function,