【摘要】：本文引入了 Base-Countably弱θ加細(xì)空間和Nearly-Meso緊空間,并且研究了這兩類空間的閉遺傳性、Tychonoff乘積性和映射性質(zhì)。獲得了如下主要結(jié)果:(1 ) {Fi}i∈N = ∪n∈N An是X的閉覆蓋,對任意x∈X存在n∈N,使得1≤ord(x,An)(?) ω ,如果任意一閉集Fi(i∈N)都是相對于X的Base-Countably弱θ加細(xì)空間,則X是Base-Countably弱θ加細(xì)空間。(2 ) f : X → Y 是 Base-Countably 弱 θ 加細(xì)映射,ω(X)≥ ω(Y),如果 Y 是正則的Base-Countably弱θ加細(xì)空間,那么x是Base-Countably弱θ加細(xì)空間。(3 ) Nearly-Meso緊空間的閉子集是Nearly-Meso緊空間。(4 ) X是Nearly-Meso緊空間當(dāng)且僅當(dāng)x的任意一單調(diào)開覆蓋U ,存在x的稠密子集D和U的一開加細(xì)U ',使得D中任意一緊集K,有(U')K是一個(gè)有限集。(5) X=Πα∈ΛXα是|Λ|-仿緊空間,那么X是Nearly-Meso緊空間當(dāng)且僅當(dāng)任α∈A意F∈[Λ](?)ω,Πα∈ΛXα是Nearly-Meso緊空間。(6)Nearly-Meso緊空間X是T3空間并且也是可數(shù)緊空間,則它是緊空間。
[Abstract]:In this paper, we introduce Base-Countably weak 胃 fineness space and Nearly-Meso compact space, and study the closed hereditary property and mapping property of these two spaces. The main results are as follows: (1) {Fi} I 鈭，

本文編號：2229680