Tej Bahadur Singh

Elements of topology

Topological Spaces Metric Spaces Topologies Derived Concepts Bases Subspaces Continuity and Products Continuity Product Topology Connectedness Connected Spaces Components Path-Connected Spaces Local Connectivity Convergence Sequences Nets Filters Hausdorff Spaces Countability Axioms 1st and 2nd Countable Spaces Separable and Lindelof Spaces Compactness Compact Spaces Countably Compact Spaces Compact Metric Spaces Locally Compact Spaces Proper Maps Topological Constructions Quotient Spaces Identification Maps Cones, Suspensions and Joins Wedge Sums and Smash Products Adjunction Spaces Coherent Topologies Separation Axioms Regular Spaces Normal Spaces Completely Regular Spaces Stone-Cech Compactification Paracompactness and Metrizability Paracompact Spaces A Metrization Theorem Completeness Complete Spaces Completion Baire Spaces Function Spaces Topology of Pointwise Convergence Compact-Open Topology Topology of Compact Convergence Topological Groups Examples and Basic Properties Subgroups Isomorphisms Direct Products Transformation Groups Group Actions Orbit Spaces The Fundamental Group Homotopic Maps The Fundamental Group Fundamental Groups of Spheres The Seifert-van Kampen Theorem Covering Spaces Covering Maps The Lifting Problem The Universal Covering Spaces Deck Transformations The Existence of Covering Spaces Appendix A: Set Theory Appendix B: Fields R, C and H Bibliography Index

_{} actions on spaces of cohomology type (,0)

A space X that has the cohomology of the one-point union P2(n) 53n or Sn VS2n VS3n is said to have cohomology type (a, 0) . Here we construct examples of free Zp actions (p an odd prime) on certain of these spaces and give a complete description of possible fixed point sets.

Stepwise equilibrium constants in copper(II)-nitroso-R-salt system a spectrophotometric study

Abstract The stepwise equilibria in the system copper(II)-nitroso- R -salt have been investigated spectrophotometrically at 25 ± 1°; the values obtained for log K 1 and log K 2 (μ = 0·1 M KNO 3 ) are 8·60 and 5·91, respectively. Molar absorptivities of the complex species CuL and CuL 2 (at 490 nm) are 487 and 12751. mole −1 mm −1 , respectively.

Cohomology ring of the orbit space of certain free _{}-actions

In this paper, we consider actions of G = Zp (with p an odd prime) on spaces X which are of cohomology type (0, 0) (i.e., have the mod-p cohomology of the one-point union of an n-sphere, a 2n-sphere and a a 3n-sphere, n odd). If X is not totally non-homologous to zero in XG we determine the fixed set, give examples of all possibilities for the fixed set and compute the cohomology ring structure of the orbit space in the case where G acts freely. In [4], we considered fixed sets for related spaces, when X is totally non-homologous to zero in XG.

Solvent extraction and spectrophotometric determination of palladium(II) with 7-iodo-8-hydroxyquinoline-5-sulphonic acid

An extractive spectrophotometric procedure has been developed for the determination of palladium (II) at microgram levels. The palladium(II) chelate of 7-iodo-8-hydroxyquinoline-5-sulphonic acid is extracted into n-butanol. Extraction is maximal (95%) from 0.2M perchloric acid. Beers law is valid at 430 nm over a wide range of palladium concentration from 2.5 ppm. The molar absorptivity is 958 1.mole(-1).mm(-1). The system can tolerate a large excess of Co(II), Ni(II), Rh(III), Pt(IV), Cr(III), W(VI), chloride, phosphate, citrate and tartrate. Small quantities of Ru(III), IR(III) and EDTA do not interfere, but serious interference is caused by Fe(III), V(V), Mo(VI) and Os(VIII).

NON-EXISTENCE OF ODD PERIODIC MAPS ON CERTAIN SPACES WITHOUT FIXED POINTS

In this paper, we show that the fixed point set of Z p -actions, p an odd prime, on a finitistic space X of type ( a , b ) is non-empty, whenever b ≡ 0 (mod p ). We also prove a similar result for circle group actions of finitistic spaces of ( a , 0) type.