Displaying similar documents to “Locally compact spaces whose Alexandroff one-point compactifications are perfect”

A generalization of Magill's Theorem for non-locally compact spaces

Gary D. Faulkner, Maria Cristina Vipera (1995)

Commentationes Mathematicae Universitatis Carolinae

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In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature...

On a perfect problem

Igor E. Zverovich (2006)

Discussiones Mathematicae Graph Theory

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We solve Open Problem (xvi) from Perfect Problems of Chvátal [1] available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex: Is there a class C of perfect graphs such that (a) C does not include all perfect graphs and (b) every perfect graph contains a vertex whose neighbors induce a subgraph that belongs to C? A class P is called locally reducible if there exists a proper subclass C of P such that every graph in P contains a local subgraph...

On near-perfect and deficient-perfect numbers

Min Tang, Xiao-Zhi Ren, Meng Li (2013)

Colloquium Mathematicae

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For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.

A basic approach to the perfect extensions of spaces

Giorgio Nordo (1997)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we generalize the notion of of a Tychonoff space to a generic extension of any space by introducing the concept of . This allow us to simplify the treatment in a basic way and in a more general setting. Some [S 1 ], [S 2 ], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.