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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2011, Number 2, Pages 17–22
(Mi basm285)
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This article is cited in 1 scientific paper (total in 1 paper)
Estimation of the number of one-point expansions of a topology which is given on a finite set
V. I. Arnautov Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
Abstract:
Let $X$ be a finite set and $\tau$ be a topology on $X$ which has precisely $m$ open sets. If $t (\tau)$ is the number of possible one-point expansions of the topology $\tau$ on $Y=X\bigcup\{y\}$, then $\frac{m\cdot(m+3)}2-1\ge t(\tau)\ge2\cdot m+\log_2m-1$ and $\frac{m\cdot(m+3)}2-1=t(\tau)$ if and only if $\tau$ is a chain (i.e. it is a linearly ordered set) and $t(\tau)=2\cdot m+\log_2m-1$ if and only if $\tau$ is an atomistic lattice.
Keywords and phrases:
finite set, topologies, one-point expansions, lattice isomorphic, atomistic lattice, chain.
Received: 24.05.2011 Revised: 21.09.2011
Citation:
V. I. Arnautov, “Estimation of the number of one-point expansions of a topology which is given on a finite set”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 2, 17–22
Linking options:
https://www.mathnet.ru/eng/basm285 https://www.mathnet.ru/eng/basm/y2011/i2/p17
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Abstract page: | 242 | Full-text PDF : | 39 | References: | 61 | First page: | 2 |
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