A remark on Baire's theorem in ranked spaces

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A remark on Remainders of homogeneous spaces in some compactifications

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

A Remark on Zoloterav’s Theorem

Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where {x} n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of γ a,n coincides with the Jacobi symbol a n if n ≡ 1 (mod 4), and 1 if n ≡ 3 (mod 4).

Remark on Loop Spaces

This theorem may be proved as an application of Stasheff's theory of yl „-spaces, and has certainly been noted by Stasheff. A method of proof was outlined in [3] in order to prove Corollary 3.12 of that paper, but the proof was defective.2 We give here a proof whose structure is essentially dual to that of the structure of the proof of Theorem A in [l], but which is much simpler in detail. Just...

Remark on a Theorem of Lindström

In a recent paper LindstrSm [I] proves a theorem on finite sets and he also proves a transfinite extension. In this note we only concern ourselves with the transfinite case of Lindstriim’s theorem. He in fact proves the following theorem: Let / Y I = K be an infinite set, and let A,, l K, be subsets of Y. Then for every p -=z m there are p disj...