ALPHA-CONTINUOUS AND ALPHA-OPEN MAPPINGS
ALPHA-CONTINUOUS AND ALPHA-OPEN MAPPINGS
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DOI：
10.1007/bf01961309
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发表时间：
1983-01-01
影响因子：
0.9
通讯作者：
ELDEEB, SN
中科院分区：
文献类型：
--
作者：
MASHHOUR, AS;HASANEIN, IA;ELDEEB, SN
设X、Y和Z是拓扑空间，除非明确说明，否则不假定分离公理。设S是X的一个子集。关闭（RESP。S的内部）将由S（resp. S~空间X的子集S称为a-集[6]（resp. [17][18][19][1 S~ S~ SOS-~一个s-集的补集（分别是半开集，预开集）称为闭集（分别为）。半闭集（semi-closed set）所有a-集的族（分别为）半开集，预开集）在X中将被表示为a（X）（分别为SO（X），PO（X））。很明显，每个c~-集（分别为a-闭集）是半开的和预开的（分别是半封闭的，预封闭的），但转换不是真的。映射f：X~ Y称为几乎连续映射[8]。0-连续[1]，弱连续[3]），简称ac（resp）。0- 100，wc）如果对于每个xCX和每个开邻域Voff（x），存在x的开邻域U使得f（U）cV-off（resp. f（U）c V，f（U）c V），称为半连续[4]（resp.前连续的[5]），简称SC（resp. pc）如果每个开集的逆像是半开的（分别为预开）。映射f：X-~ Y称为半开映射[4]（resp. preopen [5]），如果X中的每个开集的像是半开的（分别是[7]这是一个半封闭的（半开放）。预闭），如果X中的每个闭集的图像是半闭的（分别为），则X中的每个闭集的图像是半闭的（分别为）。预封闭）。
Let X, Y and Z be topological spaces on which no separation axioms are assumed unless explicitly stated. Let S be a subset of X. The closure (resp. interior) of S will be denoted by S (resp. S~ A subset S of a space X is called a-set [6](resp. semiopen set [4], preopen set [5]) if ScS~ 176 (resp. S~ S~ SOS-~ the complement of an s-set (resp. semi-open set, preopen set) is called a-closed set (resp. semi-closed set, preelosed set). The familly of all a-sets (resp. semi-open sets, preopen sets) in X will be denoted by a (X)(resp. SO (X), PO (X)). It is clear that each c~-set (resp. a-closed set) is semi-open and preopen (resp. semi-closed, preclosed), but the converses are not true. A mapping f: X~ Y is called almost continuous [8](resp. 0-continuous [1], weakly continuous [3]), briefly ac (resp. 0-cont., wc) if for each xCX and each open neighbourhood V off (x) there exists an open neighbourhood U of x such that f (U) cV-~(resp. f (U) c V, f (U) c V) and it is called semi-continuous [4](resp. precontinuous [5]), briefly sc (resp. pc) if the inverse image of each open set is semi-open (resp. preopen). A mapping f: X-~ Y is called semi-open [4](resp. preopen [5]) if the image of each open set in X is semi-open (resp. preopen) and it is called semi-closed [7](resp. preclosed) if the image of each closed set in X is semi-closed (resp. preclosed).