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Generally, the figure of the one in the cave is smaller, the growing speed is very slow and the season growing is not obvious, mainly because of lack of food and the low temperature (around 15℃) in the karst cave water. In the numerable characters, the anal fin, scale of encircle tail and gill raker of the one in the cave are in the tendency of increasing so as to adapt to the narrow water passage in the karst cave, while the length of the cave Cyprinus carpio is lengthening comparing with the one on the surface.

结果表明:从总体看洞穴鲤鱼的体形比地表鲤鱼小,生长速度缓慢,季节生长不明显,主要影响因子是洞穴内食物贫乏和水温较低(15℃左右);在可数性状中,洞穴鲤鱼的臀鳍条、围尾柄鳞和鳃耙有增多趋势,即增加了感觉细胞的附着基底;为适应洞穴水流域的狭窄通道,洞穴鲤鱼的体长相对地表鲤鱼而言有延长现象。

More precisely, under the assumptions of Dissipation, Competition and Strong Competition, we prove that there is a canonically defined countable family of unordered, disjoint invariant sets which attract all persistent trajectories whose ω-limit sets are not cycles.

的Poincaré映射,证明了在耗散性、竞争性和内部强竞争性的条件下,存在一簇至多可数个互不相交的(n-1)维不变子集吸引所有不渐近于周期轨的持续轨道。

To obtain the function and imbedding properties about relative countable tightness spaces,in this paper the question whether the relative countable tightness space can be adversely preserved by a closed map is studied by means of function and imbedding theories.

为了得到相对可数紧度空间的映射及嵌入性质,借助映射方法和紧化理论讨论了相对可数紧度空间被闭映射逆保持问题及嵌入紧空间问题,得到了相对可数紧度空间被闭映射逆保持的一个充分条件、局部紧的可数紧度空间可嵌入紧空间的几个充分条件以及某一类局部紧空间在任意紧化中不具有可数紧度等结果。

All superclasses of closed unbounded classes are stationary and stationary classes are unbounded, but there are stationary classes which are not closed and there are stationary classes which have no closed unbounded subclass ( such as the class of all limit ordinals with countable cofinality ).

所有闭合无界类的超类是固定的并且固定类是无界的,但是有着不闭合的固定类并且有着没有闭合无界子类的固定类(比如带有可数共尾性的所有极限序数的类)。

Prove that the set of odd negative integers is denumerable?

怎么样证明一个集合是不是可数集的问题?

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of , a mysterious error was found:the very same logic contradiction was applied in both Russell and Cantor's work.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系,发现康托在这两个非构造性证明中所依赖的、用对角线法所构造出的矛盾其实就是罗素悖论中所揭示的逻辑矛盾。

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proofs on the uncountability of real number set and the proof on the Cantor's Theorem of ,two mysterious errors were found: The very same idea was applied in both Russell and Cantor's work, but Cantor made wrong use of it with two logical mistakes.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系,发现康托的这两个非构造性证明与罗素悖论有完全相同的思路,但是康托犯了两个逻辑性错误而使他误用了这个悖论思路。

From the defects in the basic theory of present classical infinite theory, the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of is analyzed and a mysterious error is found:The core of Cantor's above two important proofs in set theory are actually another versions of Russell's paradox and the very same paradoxical idea was applied in both Russell and Cantor's work, and Cantor made wrong use of this paradox idea with two logical mistakes.

从经典无穷理论体系中的缺陷入手,深入分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系,发现康托在这两个证明里的核心部分实际上是罗素悖论的翻版,它们与罗素悖论有完全相同的思路,并且康托犯了两个逻辑性错误而误用了这个悖论思路。

Are countable sets:Λ-Γ,〓-Γ are either empty or countably infinite, where Γ denotes the set of γ-limit points of f; tree map's depth of attracting center is finite and the attracting center is Γ provded all the branching points are periodic points. In chapter Ⅲ. we discuss certain relationship between isolated chain recurrent point and eventually periodic point of some continua.

主要利用树的特殊偏序关系证明了:不在周期点集闭包中的ω极限点都有无限轨迹;Ω-〓,Ω-Γ为可数集,Λ-Γ,〓-Γ或为空集或可数无限,其中Γ为f的γ极限点集;当分支点都是周期点时,连续树映射的吸引中心深度有限,且吸引中心就是Γ。

This sequence is therefore not an enumeration of the set of all reals in the interval [0,1].'''This is a contradiction'''.

所以在第一点内所提出的假设&区间[0,1]中的点数是可数无穷大的&是不成立的。

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