• Korean Journal of Mathematics
• /
• 제16권4호
• /
• pp.495-498
• /
• 2008

Every totally disconnected space is hereditarily disconnected. In this note, we provide an example of a hereditarily disconnected which is not a totally disconnected space. We further provide an example that not homogeneous space is the product of a totally disconnected and a connected.

• 충청수학회지
• /
• 제1권1호
• /
• pp.65-69
• /
• 1988

In this paper dynamical properties of recurrent discrete flows are stated. The pointwise periodic discrete flows on totally disconnected spaces are of characteristic 0.

• 대한수학회지
• /
• 제59권5호
• /
• pp.987-996
• /
• 2022

We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.

• 대한수학회논문집
• /
• 제10권2호
• /
• pp.317-323
• /
• 1995

In this note we prove that Apostol's conjecture is true for the operators having totally disconnected spectra and also give a result related on compalence.

• 대한수학회논문집
• /
• 제12권3호
• /
• pp.691-699
• /
• 1997

The following statement is known as the generalized Hilbert-Smith conjecture : If G is a compact group and acts effectively on a manifold, then G is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following : A known, but has never been published before.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제10권2호
• /
• pp.4-8
• /
• 1972

We consider the class (equation omitted) of all k-degenerate graphs, for k a non-negative integer. The class (equation omitted) and (equation omitted) are exactly the classes of totally disconnected graphs and of forests, respectively; the classes (equation omitted) and (equation omitted) properly contain all outerplanar and planar graphs respectively. The advantage of this view point is that many of the known results for chromatic number and point arboricity have natural extensions, for all larger values of k. The purpose of this note is to show that a graph G is (P$^3$)-realizable if G is planar and 3-degenerate.

• 대한수학회지
• /
• 제52권2호
• /
• pp.417-429
• /
• 2015

Let R be a commutative ring with unity. The annihilator ideal graph of R, denoted by ${\Gamma}_{Ann}(R)$, is a graph whose vertices are all non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if $I{\cap}Ann(J){\neq}\{0\}$ or $J{\cap}Ann(I){\neq}\{0\}$. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose annihilator ideal graphs are totally disconnected. Also, we study diameter, girth, clique number and chromatic number of this graph. Moreover, we study some relations between annihilator ideal graph and zero-divisor graph associated with R. Among other results, it is proved that for a Noetherian ring R if ${\Gamma}_{Ann}(R)$ is triangle free, then R is Gorenstein.

• Geomechanics and Engineering
• /
• 제19권4호
• /
• pp.307-314
• /
• 2019

Light construction waste (LCW) particles are pieces of light concrete or insulation wall with light quality and certain strength, containing rich isolated and disconnected pores. Mixing LCW particles with soil can be one of the alternative lightweight soils. It can lighten and stabilize the deep-thick soft soil in-situ. In this study, the unconfined compressive strength (UCS) and its mechanism of Construction Waste Stabilized Lightweight Soil (CWSLS) are investigated. According to the prescription design, totally 35 sets of specimens are tested for the index of dry density (DD) and unconfined compressive strength (UCS). The results show that the DD of CWSLS is mainly affected by LCW content, and it decreases obviously with the increase of LCW content, while increases slightly with the increase of cement content. The UCS of CWSLS first increases and then decreases with the increase of LCW content, existing a peak value. The UCS increases linearly with the increase of cement content, while the strength growth rate is dramatically affected by the different LCW contents. The UCS of CWSLS mainly comes from the skeleton impaction of LCW particles and the gelation of soil-cement composite slurry. According to the distribution of LCW particles and soil-cement composite slurry, CWSLS specimens are divided into three structures: "suspend-dense" structure, "framework-dense" structure and "framework-pore" structure.