论文标题
计算超重空间
Counting overweight spaces
论文作者
论文摘要
令C = 2^aleph0表示连续体的基数，让A，B，K为无限的基数，使用A <b \ leq 2^a。我们表明，恰好存在A尺寸A和重量B的2^B T0空间，直至同构。在这些非塑形空间中，我们追踪 （1）2^b零维，散射，副型，完全正常的空间（如果b = 2^a）极端断开； （2）2^b连接并局部连接的Hausdorff空间； （3）2^b路径连接并局部连接，paracompact，完全正常的空间，规定\ geq c； （4）2^b连接，无处可在局部连接，完全断开，paracompact，完全正常的空间，规定\ geq c; （5）2^b散射，紧凑的T1空间； （6）2^b连接，局部连接，紧凑的T1空间； （7）2^b路径连接和散射，紧凑的T0空间； （8）2^b散射，paracompact p_k空间，每当a^{<k} = a和b^{<k} = b和2^b> 2^a时。
Let c=2^aleph0 denote the cardinality of the continuum and let a,b,k be infinite cardinal numbers with a<b\leq 2^a. We show that there exist precisely 2^b T0-spaces of size a and weight b up to homeomorphism. Among these non-homeomorphic spaces we track down (1) 2^b zero-dimensional, scattered, paracompact, perfectly normal spaces (which are also extremally disconnected in case that b=2^a); (2) 2^b connected and locally connected Hausdorff spaces; (3) 2^b pathwise connected and locally pathwise connected, paracompact, perfectly normal spaces provided that a\geq c; (4) 2^b connected, nowhere locally connected, totally pathwise disconnected, paracompact, perfectly normal spaces provided that a\geq c; (5) 2^b scattered, compact T1-spaces; (6) 2^b connected, locally connected, compact T1-spaces; (7) 2^b pathwise connected and scattered, compact T0-spaces; (8) 2^b scattered, paracompact P_k-spaces whenever a^{<k}=a and b^{<k}=b and 2^b>2^a.
