What is modal logic

General Topology-I

What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this dimension theory.

Aspects of topology: On dimension theory

Chronic sleep deficiency, defined as a state of inadequate or mistimed sleep, is a growing and underappreciated determinant of health status. Sleep deprivation contributes to a number of molecular, immune, and neural changes that play a role in disease development, independent of primary sleep disorders. These changes in biological processes in response to chronic sleep deficiency may serve as etiological factors for the development and exacerbation of cardiovascular and metabolic diseases and, ultimately, a shortened lifespan. Sleep deprivation also results in significant impairments in cognitive and motor performance which increase the risk of motor vehicle crashes and work-related injuries and fatal accidents. The American Academy of Sleep Medicine and the Sleep Research Society have developed this statement to communicate to national health stakeholders the current knowledge which ties sufficient sleep and circadian alignment in adults to health.

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Sleep: a health imperative.

The combinatorial study of subsets of the set N of natural numbers and of functions from N to N leads to numerous cardinal numbers, uncountable but no larger than the continuum. For example, how many infinite subsets X of N must I take so that every subset Y of N or its complement includes one of my X’s? Or how many functions f from N to N must I take so that every function from N to N is majorized by one of my f’s? The main results about these cardinal characteristics of the continuum are of two sorts: inequalities involving two (or sometimes three) characteristics, and independence results saying that other such inequalities cannot be proved in ZFC. Other results concern, for example, the cofinalities of these cardinals or connections with other areas of mathematics. This survey concentrates on the combinatorial set-theoretic aspects of the theory.

Combinatorial Cardinal Characteristics of the Continuum

This is a cumulative status report on the 1100 problems listed in the volume Open Problems in Topology (North-Holland, 1990), edited by J. van Mill and G.M. Reed.

Open Problems in Topology

Introduction. Chapter 1. Basic topology. Chapter 2. Basic combinatorial topology. Chapter 3. Basic dimension theory. Chapter 4. Basic ANR theory. Chapter 5. Basic infinite-dimensional topology. Chapter 6. Function spaces. Appendix A. Preliminaries. Appendix B. Answers to selected exercises. Appendix C. Notes and comments. Bibliography. Special Symbols. Author Index. Subject Index.

http://www.gbv.de/dms/goettingen/329171577.pdf

The Infinite-Dimensional Topology of Function Spaces

1. Extension Theorems. Topological Spaces. Linear Spaces. Function Spaces. The Michael Selection Theorem and Applications. AR's and ANR's. The Borsuk Homotopy Extension Theorem. 2. Elementary Plane Topology. The Brouwer Fixed-Point Theorem and Applications. The Borsuk-Ulam Theorem. The Poincare Theorem. The Jordan Curve Theorem. 3. Elementary Combinatorial Techniques. Affine Notions. Simplexes. Triangulation. Simplexes in Rn. The Brouwer Fixed-Point Theorem. Topologizing a Simplical Complex. 4. Elementary Dimension Theory. The Covering Dimension. Zero-Dimensional Spaces. Translation into Open Covers. The Imbedding Theorem. The Inductive Dimension Functions ind and Ind. Mappings into Spheres. Totally Disconnected Spaces. Various Kinds of Infinite-Dimensionality. 5. Elementary ANR Theory. Some Properties of ANR's. A Characterization of ANR's and AR's. Hyperspaces and the AR-Property. Open Subspaces of ANR's. Characterization of Finite-Dimensional ANR's and AR's. Adjunction Spaces of Compact A(N)R's. 6. An Introduction to Infinite-Dimensional Topology. Constructing New Homeomorphisms from Old. Z-Sets. The Estimated Homeomorphism Extension Theorem for Compacta in s. The Estimated Homeomorphism Extension Theorem. Absorbers. Hilbert Space is Homeomorphic to the Countable Infinite Product of Lines. Inverse Limits. Hilbert Cube Factors. 7. Cell-Like Maps and Q-Manifolds. Cell-Like Maps and Fine Homotopy Equivalences. Z-Sets in ANR's. The Disjoint-Cells Property. Z-Sets in Q-Manifolds. Torunczyk's Approximation Theorem and Applications. Cell-Like Maps. The Characterization Theorem. 8. Applications. Infinite Products. Keller's Theorem. Cone Characterization of the Hilbert Cube. The Curtis-Schori-West Hyperspace Theorem. What Next? Bibliography. Subject Index.

Infinite Dimensional Topology: Prerequisites and Introduction

A K ATP channel gene effect on sleep duration: from genome-wide association studies to function in Drosophila

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A K(ATP) channel gene effect on sleep duration: from genome-wide association studies to function in Drosophila.

Topological Homogeneity.- Some Recent Progress Concerning Topology of Fractals.- A biased view of topology as a tool in functional analysis.- Large scale versus small scale.- Descriptive aspects of Rosenthal compacta.- Minimality conditions in topological groups.- Set-Theoretic update on Topology.- Topics in Dimension Theory.- Representations of dynamical systems on Banach spaces.- Generalized metrizable spaces.- Permanence in Coarse Geometry.- Selections and Hyperspaces.- Continuum Theory.- Almost disjoint families and topology.- Some Topics in Geometric Topology II.- Topological aspects of dynamics of pairs, tuples and sets.- Continuous selections of multivalued mappings.- The combinatorics of open covers.- Covering properties.- Paratopological and semitopological groups vs topological groups.

J. van Mill

Papers

Open Problems in Topology

The Infinite-Dimensional Topology of Function Spaces

Infinite Dimensional Topology: Prerequisites and Introduction

A K(ATP) channel gene effect on sleep duration: from genome-wide association studies to function in Drosophila.

Recent progress in general topology.