SPRITE SPACE: Some submissives will squirm and utterly deny that this space exists. If the Dominant mentally presses.she will generally descend further into space.
SUBSPACE DEFINITION FULL
Or, go back to full functional top space. If nothing further occurs she will most likely re-top. She will generally attempt direct eye contact with her Dominant to see if he/she has a direction or command for her. Generally she will cease talking even in the midst of a comment. This marginal appearing contact drops the submissive out of top space into a state of waiting and/or listening for command. This may be a glance, a light touch, a small sound or any combination of these triggers. MARGINALLY DOWN SPACE: This space occurs when the Dominant in the relationship directs attention at the submissive. They are the Commander of the ship, the General of the Army. They will be hustling their children off to school, dominating their Dominant mate by organizing him/her off to work, cleaning and straightening the house, sending themselves off to work or to take care of business.
The submissive in top space often appears quite aggressive, assertive and dominant. TOP SPACE: I will start by regarding top space or normal space.
Subspace - This term generally is used to describe a moderate to deep trancelike condition experienced by persons in the submissive position in a D/s relationship during interaction with the person in the Dominant position in the relationship. It was part of her Steel’s Chamber Scrolls which is now defunct. Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics) by I.The subspace topology is the coarsest topology that can be endowed on, for which the inclusion map from to is a continuous map.įurther information: Equivalence of definitions of subspace topology References Textbook references To show that this is true, we show equivalence with the open subset formulation. Thus, a priori, it is not clear that different starting choices of basis for would yield the same topology on. Note that while a subbasis uniquely determines the topology, the same topology can be described by different possibilities for basis. In other words, if form a subbasis for, then a basis for the subspace topology on is given by. Namely, for each subbasis open set, replace it by its intersection with. Given a subbasis for, we can directly use it to define a basis for the subspace topology on. Note that while a basis uniquely determines the topology, the same topology can be describd by different possibilities for basis. In other words, if form a basis for, then a basis for the subspace topology on is given by. Namely, for each basis open set, replace it by its intersection with. Given a basis for, we can directly use it to define a basis for the subspace topology on. The description of which subsets are closed completely determines the topology, and the topology completely determines which subsets are open.Īlso, is not uniquely determined by, though, subject to its existence, we can take a minimal, which is the intersection of all possible choices, and is also the closure of within. In other words, is closed in if and only if there exists a closed subset of such that. Ī subset of is closed in if and only if it is the intersection with of a closed subset of. The description of which subsets are open completely determines the topology, and the topology completely determines which subsets are open.Īlso, is not uniquely determined by, though, subject to its existence, we can take a maximal, which is the union of all the possible choices for. In other words, is open in if and only if there exists an open subset of such that. The equivalent formulations are described below:Ī subset of is open in if and only if it is the intersection with of an open subset of. The subspace topology can be defined in many equivalent ways. Thus, subsets of topological spaces are often also called subspaces. Note that induced with this topology is a topological space in its own right. The subspace topology or induced topology or relative topology on can be defined in many equivalent ways. Let be a topological space (viz, a set endowed with a topology ) and be a subset of. View other induced structures on subspaces Definition View a complete list of basic definitions in topology This article describes the induced structure on any subset (subspace) corresponding to a particular structure on a set: the structure of a topological space VIEW: Definitions built on this | Facts about this | Survey articles about this This article is about a basic definition in topology.
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