Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 36.

Chan Ka Wo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 114-118). / Abstracts in English and Chinese. / Introduction --- p.iii / Conventions of This Thesis --- p.vi / Prerequisites --- p.xiii / Chapter 1 --- Cones in Real Vector Spaces --- p.1 / Chapter 1.1 --- The Fundamentals of Cones --- p.2 / Chapter 1.2 --- Enlargements of a Cone --- p.22 / Chapter 1.3 --- Special Cones in Real Vector Spaces --- p.29 / Chapter 1.3.1 --- Positive Cones --- p.29 / Chapter 1.3.2 --- Bishop-Phelps Cones --- p.36 / Chapter 1.3.3 --- Quasi-Bishop-Phelps Cones --- p.42 / Chapter 1.3.4 --- Quasi*-Bishop-Phelps Cones --- p.45 / Chapter 1.3.5 --- Gallagher-Saleh D-cones --- p.47 / Chapter 2 --- Generalizations in Topological Vector Spaces --- p.52 / Chapter 2.1 --- Efficiency and Positive Proper Efficiency --- p.54 / Chapter 2.2 --- Type I Generalizations --- p.71 / Chapter 2.3 --- Type II Generalizations --- p.82 / Chapter 2.4 --- Type III Generalizations --- p.92 / Chapter 3 --- Generalizations in Dual Spaces --- p.97 / Chapter 3.1 --- Weak*-Support Points of a Set --- p.98 / Chapter 3.2 --- Generalizations in the Dual Space of a General Normed Space --- p.100 / Chapter 3.3 --- Generalizations in the Dual Space of a Banach Space --- p.104 / Epilogue: Glimpses Beyond --- p.112 / Bibliography --- p.114

設T為一於二維環面T²上，特徵值為整數的線性自同態，而D為一T²的Markov分割。那麼每一個D上定義的符號空間有限型子轉移則對應一個T²的T -不變緊子集K。判斷K的 Hausdor和Minkowski維數何時相等是一有趣問題。Kenyon and Peres [15]說明了此問題與(K, T )的測度熵及拓撲熵關係密切。這篇論文將進一步說明兩種維數的相等與符號動力系統及矩陣乘積的漸近性態的密切關係。此外我們描述一種算法以判斷兩個譜半徑為1的本原矩陣的任意乘積的譜半徑何時維持1，以及此算法對於研究sofic自仿集K的應用。 / Let T be a linear endomorphism on the 2-torus T² with integer eigenvalues, and D be a natural Markov partition (c.f. Bowen [4]) of T² . Then a subshift of nite type over D corresponds to a T-invariant compact subset K of T². An interesting problem is to determine when the Hausdorff and Minkowski dimensions of K conincide. Kenyon and Peres [15] showed that this is closely related to the measure-theoretic and topological entropies of (K, T). In this thesis, we further show that the coincidence of dimensions has a deep connection to symbolic dynamics and the asymptotic behaviour of matrix products. Moreover, we develop an algorithm to determine when the spectral radii of arbitrary products of two primitive matrices, with spectral radius 1, are preserved, and apply this algorithm to some sofic self-affine sets considered above. / Detailed summary in vernacular field only. / Lo, Chiu Hong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 55-56). / Abstracts also in Chinese. / Chapter 1 --- Introduction and Main Results --- p.6 / Chapter 2 --- Preliminaries --- p.12 / Chapter 2.1 --- Basic symbolic dynamics --- p.12 / Chapter 2.2 --- The symbolic representations --- p.13 / Chapter 2.3 --- An adapted covering of the invariant set KT (A) --- p.17 / Chapter 2.4 --- Some basic lemmas and theorems --- p.18 / Chapter 3 --- Proofs of Proposition 1.2 and Theorem 1.3 --- p.22 / Chapter 3.1 --- Proof of Proposition 1.2 --- p.22 / Chapter 3.2 --- Proof of Theorem 1.3 --- p.24 / Chapter 4 --- Projection of measure of maximal entropy for sub-shifts of finite type --- p.26 / Chapter 4.1 --- Projection of the Parry measure via a general factor map --- p.26 / Chapter 4.2 --- Proof of Theorem 1.4 --- p.36 / Chapter 5 --- Spectral radii of products of primitive matrices --- p.38 / Chapter 5.1 --- The algorithm --- p.40 / Chapter 5.2 --- Some applications and examples --- p.51 / Bibliography --- p.55

Explores topological spaces, filters, and nets with definitions and examples.

Thesis (Ph.D.)--Ohio University, August, 2009. / Release of full electronic text on OhioLINK has been delayed until September 1, 2012. Includes bibliographical references (leaves 110-113)

Thesis (Ph.D.)--Ohio University, August, 2009. / Title from PDF t.p. Release of full electronic text on OhioLINK has been delayed until September 1, 2012. Includes bibliographical references (leaves 110-113)

Thesis (Ph.D.)--Ohio University, August, 2009. / Release of full electronic text on OhioLINK has been delayed until June 1, 2012. Includes bibliographical references (leaves 63-66)

Thesis (Ph.D.)--Ohio University, August, 2009. / Title from PDF t.p. Release of full electronic text on OhioLINK has been delayed until June 1, 2012. Includes bibliographical references (leaves 63-66)

There are many different notions of stratified spaces. This thesis concerns homotopically stratified spaces. These were defined by Frank Quinn in his paper Homotopically Stratified Sets ([16]). His definition of stratified space is very general and relates strata by “homotopy rather than geometric conditions”. This makes homotopically stratified spaces the ideal class of stratified spaces on which to define and study stratified homotopy theory. In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those spaces of popaths which immediately leave a lower stratum for their final stratum destination). It is not immediately clear that for adjacent strata these two path spaces are homotopically equivalent and even less clear that this equivalence can be constructed in a useful way. The first aim of this thesis is to prove such an equivalence exists for homotopically stratified spaces. We will define stratified analogues of the usual definitions of maps, homotopies and homotopy equivalences. Then we will provide an elementary criterion for deciding when a strongly stratified map is a stratified homotopy equivalence. This criterion states that a strongly stratified map is a stratified homotopy equivalence if and only if the induced maps on strata and holink spaces are homotopy equivalences. Using this criterion we will prove that any homotopically stratified space is stratified homotopy equivalent to a homotopically stratified space where neighborhoods of strata are mapping cylinders. Finally we will develop categorical descriptions of the class of homotopically stratified spaces up to stratified homotopy. The first of these categorical descriptions will involve categories with a topology on their object and morphism sets. The second categorical description will involve only categories with discrete object spaces.

No description available.