A note on D-spaces

We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that C_p(X) is hereditarily a D-space whenever X is a Lindel\"of \Sigma-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact. We also prove that if a space X is the union of finitely many D-spaces, and has countable extent, then X is linearly Lindel\"of. It follows that if X is in addition countably compact, then X must be compact. We also show that Corson compact spaces are hereditarily D-spaces. These last two results answer recent questions of Arhangel'skii. Finally, we answer a question of van Douwen by showing that a perfectly normal collectionwise-normal non-paracompact space constructed by R. Pol is a D-space.Comment: 11 page

The Collins-Roscoe mechanism and D-spaces

We prove that if a space X is well ordered $(\alpha A)$, or linearly semi-stratifiable, or elastic then X is a D-space

Diagram spaces, diagram spectra, and spectra of units

This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor \Omega^\infty. We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors \Omega^\infty agree. This comparison is then used to show that two different constructions of the spectrum of units gl_1 R of a commutative ring spectrum R agree.Comment: 62 pages. The definition of the functor \mathbb{Q} is changed. Sections 8, 9, 17 and 18 contain revisions and/or new materia

Differential Structure of Space-Time and Physical Fields

A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness of the scalar field leads either to modification of cosmic string's space-time global properties or to quantization of the deficit of angle: $\Delta =2\pi (1-1/n)$, $n=1,2,\dots$.Comment: 9 pages, LaTeX, Lecture delivered at " Workshop on Modern Methods in Classical and Quantum Gravity ", July 26-28th, 1995, Sintra, Portuga

On weakly monotonically monolithic spaces

Abstract. In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a D-space. Thus most known conclusions on D-spaces can be obtained by this conclusion. As a corollary, we have that if a regular space X is sequential and has a point-countable wcs * -network then X is a D-space

On the Singularities of Reissner-Nordstr\"{o}m Space-Time

It is shown that if two Reissner-Nordstr\"{o}m space-times, both with the same mass m and charge e, glued together in the singularities, then the light ray in black hole of the first space-time can go continuously through the singularity into black hole of the second. The behavior of tidal forces near the Reissner-Nordstr\"{o}m space-time singularity is examined by considering what happens between two particles falling freely towards the singularity.Comment: Latex, 4 figures, 11 page