Countable compactifications of topological spaces have been studied in [1], [5], [7], and [9]. In [7], Magill showed that a locally compact, T2 topological space X has a countable T2 compactification if and only if it has n-point T2 compactifications for every integer n ≥ 1. We generalize this theorem to T2-ordered compactifications of ordered topological spaces. Before starting our generalizat...

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is σ-compact. Also, the existence of a Scheepers non-σ-compact remainder of a topological group follows from CH and yields a P -point, and hence is independent of Z...

A generalization of the pre-Grüss inequality is presented. It is applied to estimations of remainders of some quadrature formulas.

We introduce the notions of unsigned and signed generalized Lucas sequences and prove certain polynomial recurrence relations on their characteristic polynomials. We also characterize when these characteristic polynomials are irreducible polynomials over a finite field. Moreover, we obtain the explicit expressions of the remainders of Dickson polynomials of the first kind divided by the charact...

From EXAFS spectra of As and As2O3 vapors and arsine gas AsH3 the ab initio calculated structural signal is removed. The remainders comprise small absorption edges due to shake-up channels involving electrons from 3d or 3p subshell. With enhanced resolution, the edges reveal a fine splitting and a varying contribution of resonance channels, due to individual molecular energy-level structure of ...

This paper proposes an efficient frequency estimator based on Chinese Remainder Theorem for undersampled waveforms. Due to the emphasis on frequency offset recognition (i.e., frequency shift and compensation) of small-point DFT remainders, compared to estimators using large-point DFT remainders, it can achieve higher noise robustness in low signal-to-noise ratio (SNR) cases and higher accuracy ...

Are two compactifications of ω homeomorphic if their remainders are homeomorphic? For metrizable compactifications the question was answered affirmatively by Pelzcynski. Can the same happen for some non-metrizable remainders? We consider the case when the remainder is D for some uncountable τ . We show that the answer is affirmative if τ < p and negative if τ = c. We prove that every isomorphis...